You could add some more depth by lets say having a specialization-tree with unlockables that require some level in the general skill.
I like this idea! Knowing that as the game designer you must plan out every step of every branch of that tree, having a special move/buff at certain levels of advancement can encourage specialization. Deep knowledge of a specific weapon might let you know that every 5th shot of continuous automatic fire from that make/model has a high % chance to cause a jam. This could translate into a bonus to reduce or eliminate that % chance because you know how to maintain the weapon to keep the jam from happening.
A bonus for the pistol line could be explained that by studying the use of the pistol so much, the character reflexively knows the proper forms and uses for that class of weapon. This leads to unlocking trick shots and advanced tactics available to them in gameplay at various levels.
I'm thinking that you are looking more for a system like (but not exactly like) Star Wars Galaxies where there was an overall combat class, but could specialize down certain weapon-type paths to get specific skills when using that class of weapon.
I'm just thinking out loud here...