I don't think PDW should be a category on its own, group it with rifles if you want the difference to be how many hands are needed to use the weapon, or pistols if it's more ammo/penetration/portability related. If PDW end up with pistols (avoids letting rifle skill get all the fun) I suggest that a PDW can be fired one-handed, but at +1 recoil and range changed to pistol (assuming the weapon has assault range).
As for shotguns, why are they more different from rifles than a musket is from a gauss rifle? Now, I understand that someone, say a hunter, could train with a shotgun but never hold an assault rifle, but if that's the case some single-shot hunting rifles should be included too (and perhaps even bows/crossbows?) and the skill could be called Hunting or civilian instead (though civilian should perhaps include some pistols too). Or, since shotguns launch special types of ammo and handle differently from a typical assault rifle, perhaps move handheld grenade/RAM launchers from heavy to shotgun?
Laser Carbines should be included in energy rifles, IMO.
If you end up with lots of skills, they could perhaps relate more to each other? E.g if I have slug rifle 2 I can use a carbine at (rifle-1) instead of 0?
As for the new AP and destructive, sounds good. AP is a bit more rare than before, but easy to use from the tables, though is destructive too... well, destructive? Should it perhaps treat armor points as additional hull points that gets eaten away first, and then the usual vehicle damage table is used? Nah, probably not, I just feel that a heavy armored tank might be a little better off compared to a regular car, otherwise destructive might as well mean "remove target from play".
As for small spacecraft versus ground vehicles, well... It is a bit weird that a 20 ton shuttle built with ship rules is invincible to "all" ground weapons, while its puny beam laser can lay waste to anything in sight, while a similar craft built from supp 5-6 doesn't stand a chance against it. Like a Manta from Dredd, if it was built as a small spacecraft with a beam laser and some personal scale weapons it'd be indestructable, now a 20 ton launch can one-shot it...