Related question: If I arm my drone with a Yamaha Raiden, what type/how many Targeting Autosofts does it require in order to function fully? This is an assault rifle with underbarrel grenade launcher and shotgun.
An interesting scenario to parse. IMO the first thing to rule on is whether there's one underbarrel weapon that fires either shotgun shells or grenades, or two underbarrel weapons. I prefer to envision that it's one weapon that can employ either ammo type.
Now in the case of which skills "should" cover all this... I think it's obvious that Firearms (Rifles) governs the "main gun". As for the underbarrel weapon, I'd say it depends on which ammo is loaded. Shotgun shells? Ok, you use Firearms (Shotguns). Grenades? Now it's Exotic (Grenade Launchers).
That's how I see the Skills answer. Skills are not 1:1 comparable to Autosofts, however. 1) Skills are very broad, while Autosofts are only applicable to a single weapon. 2) The opportunity cost in accumulating skills is not comparable. Mechanically, nothing stops you from employing every skill in the book, provided you had enough Skill points/Karma to get there. OTOH even if you have infinite nuyen, you have a hard cap on how many Autosofts a vehicle/drone can have running simultaneously. So just because it follows that the Raiden should use multiple skills to use all its capabilities, in the case of Autosofts I'm very sympathetic to the view that "one weapon uses one Autosoft". Afterall, a Targeting Autosoft is useless on everything outside that one weapon, it really would suck hard if it didn't even allow full use of that one weapon.
Now in the case of underbarrel weapons that are NOT factory standard/integral: I'm fine with requiring multiple Autosofts. It's a munchkin tax. If you want to use that (perfectly legal) loophole to put 2 weapons in one weapon mount, it's only fair you "pay" for that via having to use multiple Targeting Autosofts in THIS case. Yes, it's a fully meta rationale... if you don't accept meta rationales then this is the in-universe one: The software for Targeting Autosofts don't account for crazy aftermarket stuff you do to the gun. You pack a gun on your gun, that's 2 guns as far as software is concerned. Guns like the Raiden that were engineered that way are different- the software was already written to include it.
Edit: Lol, Banshee showed how I shoulda TL;DR'd my opinions here:
Skills: Multiple.
Autosofts: One.
Autosofts on aftermarket UBGLs rather than an integral one like in the case of a Raiden: Multiple.