Hey Strogg, welcome to the forums.
Indeed new weapons would be great, and the examples you bring are great, but unfortunately i doubt Styg will be adding any more due to how much it would cost.
I disagree with your second suggestion, though.
and while light stealth characters are feasible, that is only if you build your initial stats to allow for the more powerful feats in the game as you progress (e.g cut throat).
I consider my stealthy knife&traps specialist a light stealth character, and he is 8-8-8-5-3-3-5.
Whats wrong with going with a high dexterity stat, for the cut throat feat, if you are already doing a "dexterity based" melee character?
Light melee weapons (i.e one handed) should also receive a damage bonus from dexterity, but only if it is greater than strength.
Why? Then the only reasons for pumping strength would be:
-The Sledgehammer
-The Metal Armor
-Full-auto feat (the only feat that requires strength)
With the exception of intelligence, every stat is pretty much balanced. What you purpose would make strength almost useless.
I believe you are being inspired by the Weapon Finesse feat from D&D that allows a character to add his dex modifier, instead of his str modifier, on attack rolls ( to hit chance ). And although this feat provides more hit chance, with melee weapons for dex based characters, it wont grant them more damage. So if they have a low strength stat, it wont do them much good (unless you are going for something like a duel wielding kukri critical build).
Imagine that we could use Will instead of Perceptions for shooting, inspired by the Zen Archery, another D&D feat.
If you wanted to make a psy gunner/crossbow-guy you could just ditch perception and be fine.
Now this kind of solutions might work with D&D but not so much in rpgs like underrail.
There are already so many stats that you can ignore when going for a pure melee build (intelligence, perception, will, agility) and adding the most important melee stat to that list just seems unreasonable.