Do you need to be proficient with a weapon to load it? It's not a roll-related thing, so no proficiency bonus doesn't matter, so you should be able to.
Good catch on the "has hands" part too. Opens up a lot of options compared to most normal pets. Even some ranged attacks for dexxy creatures (there is no proficiency or training needed for some of them, ala alchemist's fire or acid flasks. It's an action, not an "attack action". Damage-type versatility is good for any pet). Yet another caltrop/ball bearing delivery system is nice too. Something as simple as a giant spider becomes way more useful with hands. At worst, everything's a crappy bowman (assuming your DM plays it that everything can use its action to "attack", unless stated otherwise). Even two weapon fighting is possible in theory (although virtually everything is 2d6+Str or better to begin with anyway, often with higher to-hit than basic stats give you). You're not losing a proficiency bonus if you didn't have any in the first place. It's hands you need, not training. Throwing, shooting and melee is all "allowable" with the necessary appendages. It's just potentially worse than the beast's normal attack actions. Pack Tactics' advantage may smooth out to-hit rolls with two weapons though. And you've got slashing/bludgeoning/piercing damage at all times with enough hands too. Everything gets a crappy reach attack as well.
It shouldn't be exactly hard to armour them up a bit if you base them on a warhorse for armour "proficiency" either. Not the best HP-wise, and "appropriate for its statistics" is kind of a grey area, but there's tonnes of options with hands and "look how you want".
So many options. Body double pets, exact copies of kings, 34 tentacle-hand hentai thingies, the list list goes on. Large size stymies a few of these, but they're just examples. It could be a walking (or flying) mini-fort, a stealth-boulder, a large flying piece of rope (with many hands, talons and a beak), or anything you can imagine really.
"Appropriate for its statistics" is such a silly term in D&D.
((don't know if the above action sequence would fly with some DMs. Attacks tend to be made all in one go, so having a "free action" in between them that interacts with something else might not be allowed. Which is kind of silly considering the lack of movement restrictions, etc, with multiple attacks, but there you go. It may be allowed for the very same reasons. Depends on if your DM thinks grabbing a weapon from someone else is "free" on step #3. Drawing a weapon is different to grabbing one from someone else, especially if you've already attacked with and dropped one already. "Free" actions are meant to smooth over stuff, not give unlimited time-independant interactions. When you take your bonus action at step #5 is also a problem, because they tend to happen on "your turn", not whenever you feel like it. Could just switch steps #4 and #5 to alleviate that though. This is hypothetically. I wouldn't let you "lose" your thunder gun like that anyway.))