Possibly they could be Handgun, Longarm, and Heavy. The skill to use would be determined not by the weapon, but how you are using the weapon...
For example, you have a SMG with retractible stock. With the stock retracted, firing from the hip, you use handgun skill. With the stock extended, firing from the shoulder, you use Longarm. If firing from a bipod or tripod, (god knows why, but go with me here.) you would use Heavy.
I would double the cost to purchase the skill at both chargen and in game, since each skill is broader.
Then I would borrow the mechanic of Centering skills to customize the use of the skills. They would share nothing besides the game mechanics with magical centering. These centering skills would be oriented towards situations you would use a weapon in, and would not be combinable.
some centering examples (lots of brainstorming here):
Sniper Helps with range penalties, movement at range, etc
CQB Not sure here, perhaps reaction bonuses at close range
Support stuff like autofire recoil.
Very much a work in progress here. Think it might be worth pursuing further?
