I suppose it'd end up being two skills, really - which, on further thought, most crafting skills would have: Modification and Construction.
Modification is pretty simple. Giving a gun a bigger clip. Adding nails to a bat. Mixing flavorings into drinks. It can get fancier, but it's all just expanding on a base model.
Construction, on the other hand, is the production of a base model. Making things as opposed to just making them better.
In the context of Heavily Improvised Weaponry, you'd probably have a wider range of things you could make and mod than most crafting skills, but you wouldn't be able make things as powerful. A flamethrower made by a guy who makes flamethrowers is generally going to be better than a flamethrower made out of a leafblower, a tank of petrol, and grill parts, basically.