Of course leaving reach out of this to me would be an issue. Yeah knives are faster but don't reach far. A big 2 hander can touch you a little ways more out.

I have found from my limited personal experience that without a ton of training having a knife means you lose against a sword. Reach makes a huge difference and has to be figured in if you go for a detailed system.

but once again just my thoughts

To reiterate we really don't have too much info about the base combat system that jibba wants to work from. I gather it's EXACTLY LIKE AD&D except for armor absorbs and maybe to-hit doesn't vary by AC. If there's more, we need to know.

Also, the devil is often in the details rather than the overall shape of the solution. As pointed out if you want to have multiple attack rolls stand in for "speed" then the issue is the scale of strength bonus and armor DR. Yes, you can patch this by limiting strength bonus for smaller weapons.

Furthermore a minmaxed character who has multiple attacks and a high damage bonus is simply someone who is both strong and fast. The EFFECT is the thing itself, especially in highly abstracted systems such as D&D combat. Looking at the inputs just obscures the matter.

Miscellaneous notes: for weapon reach I would check Runequest (3e, maybe the later ones, possibly BRP or OQ) which have rules for holding a person at bay with a longer weapon and closing with a shorter weapon within the reach of an opponent. BW may also have something like this but in my reading of BWR it was a mess. For an interesting approach to armor you could look at Palladium 1e (I know nothing of the others) which as I recall made it valuable for low-level characters but less important as you became more skillful. The details elude me at the moment.

Note that the niche of various weapons isn't just tactical environment but other factors. A dagger isn't superior to a sword tactically, pretty much ever. It just sucks less comparatively when facing an unarmored opponent and it has advantages which are extrinsic to the toe-toe confrontation such as cost, concealability, and acceptability to the local law-level. That is why it's a good assassin's weapon, not because of some crazy dagger-fu. The same is also largely what's going on with rapiers. The hand-hand weapon of infantry in the gunpowder age was the _____. (Hint: the answer is not rapier.)

If you want dagger-fu, by all means but bear in mind you're after a certain effect, not a cause.

The base is mongoose traveller.

the Gurps stuff looks useful I will try to grab a copy and adapt some of it.
I don;t want dagger-fu I actually want to avoid dagger-fu being too powerful.

The combat system is I guess pretty standard

You roll 2d10 with a base target number of your opponents defense (13 being the base)
You get an attack bonus this varies depending on how players choose to develop as they level but a fighter gets +1 per level, a rogue +1/2 levels and a magus/psker (depending on genre) +1/3 levels. All classes can add to this as they advance upto 1 more point per level from a pool of points they can spend on a host of stuff. As an example our 5th level fighter has +7 attack.
You get a defensive bonus which rises at the same rate as attack, but remember there is some customisation as you level. Our 5th level fighter has +6 defense.

So far so basic 2d10 + attack vs defense

Initiative is 1d10 + dex.
There is an optional rule for weapons speed and reach.
Weapon speed work as per AD&D so the higher speed is slower and this subtracts from the initiaitve roll.
Reach comes in 4 categories. Very long (pikes), Long (spears pole arms), medium (swords) and short (daggers and shortswords). Attacking someone with a longer weapon means you take an AoO unless you have a combat move to avoid it. Subsequently the longer reach weapon can attempt to step back whcih is an opposed roll if they don;t then they are at DISADVANTAGE whcih can stack to -3 (roll 5 dice take lowest 2 for pike versus dagger at close quarters)
Now in our current game we haven't been using either of those rules as they slow us down. However I break them out whenever a combat becomes "significant", that is to say when the opponent is a major chanracter, when the PC is injured and so combat could easily be lethal, or when I feel a memorable tactical battle suits the mood of the table (I can see some folks might find this too narative/dramatic).

Armour absorbs damage. it ranges from 1-15 in defense with some typical values being leather=2, chain=5, plate=8-10, Kevlar=5, Power Armour or magical =15.
There are 10 hit locations and armour is described, so a Chain Hauberk covers your torso and arms and legs to a lesser extent. the Hit locations are then averaged to give a generic AC. this generic score is what you use 90% of the time with the location dice only being added when a combat is "significant".

Damage is worked from d6's. A dagger does 1d6 a sword does 2d6 a two handed sword or battleaxe does 3d6. There is variation in the example I mentioned from this weeks game with the new PC using 2 vibra blades which are daggers with vibrating monofilamant edges, such things being the bread and butter of the 2000ad-esque universe the game is set in.
Strength dgives a damage bonus generally. However, there are some special combat options that may allow variation here.

Combat manuvers/feats are handled through weapons styles. There are a bunch of weapons styles, unarmed, knife fighting, sword and shield, two handed, polearm/spear, fencing, kenjitsu, archery, mounted melee, mounted archery etc etc and in the modern variant, pistol, rifle, heavy weapons etc...
You can put upto 5 ranks in each weapon style, you start with 1,2 or 3 you buy them from your points as you level. additional ranks give you benefits. So if you have 2 ranks in knife fighting you can use 2 knives with no pentalty, if you have 1 rank in shield you can opt to block any strike within 2 of your defense and the shield takes the hit etc etc ... This means you have combat options but without the millions of possible broken combos. basically each style has a set progression.
No styles give default attack bonuses but some do give damage bonuses, 2 ranks in two handed for example gives a +2 damage bonus.

Finally Hit points. Hit points are ablative and fast to recover. Under hit points are wounds.
So a fighter has 10 hp at 1st level + con (remember max con is +5) . Then they gain 1hp per level but can buy additional HPs, a rogue 8 points +1/2levels a magus 6 +1/3 levels. As a comaparison our 5th level warrior has 18 hp our 5th level Psyker/magus has 10.
Wounds run into a death spiral down to 7 wounds = dead.
HPs recover 1 point every 5 minutes rest and you can in combat take no action to make a Con check (roll 2d10+con vs 13) to regain a HD (d10,d8,d6).

Most modifiers are rolled into advantage and disadvantage which can stack 3 deep. this was added after Next because it got rid of loads of petty annoying old school style modifiers that just slowed down combat.

So in combat a guy with 2 daggers with 2 ranks in knifefigthing will get 2 attacks (dual wield) if they have 4 ranks they will get 4 attacks (additional attack is the 4th rank effect). If the opponent is not armoured and has low defense this is lethal if they have say chain armour then knives cease to be effective unless the attacker has a high damage  bonus (note the 5th rank of knife fighting the knife fu if you will allows you to use your dex as a damage bonus and this may be broken) because the knife does 1d6 and chain has AC5.  
A guy with a battle axe with 2 ranks would be doing 3d6+2 + damage bonus. so their 1 hit will be far more effective against a guy in chain. 5 defense versus 3d6+2.