I don't think you will find any explicit text on this
I don't see anything disallowing undead from using wands. Personally I would say zombies are too dumb. But that is my interpretation of the Mindless Soldiers, maybe wands are just as easy to use as weapons.
Skeletons I would say yes, they can use tools, so why not magical tools?
Attunement is much the same deal, there is no reason in the rules a skeleton or zombie shouldn't be allowed to attune.
Here are some tweets by Jeremy Crawford discussing undead and magic items.
Personally, I would not allow it, saying that you need a charisma of 6 or higher to enforce your will on a magic item. (This would be a house rule though)
Do note that most wands require attunement by a spellcaster. Though wand of magic missiles can be dangerous enough, if he can get his hands on enough of them.
Advice on how to proceed
What I would do
- Allow it for skeletons and not for zombies.
- Make sure there is a lot of AoE capabilities among the enemies.
- Limit the supply of wands that does not require attunement by a spellcaster. To my knowledge the only offensive wand that does not require attunement is wand of magic missile, if there are others, I would think really hard before allowing those into the game.
- Use the shield spell a bunch. It negates magic missile completely, but also spends the targets reaction, preventing it from counterspelling the players important spells. (I play with optimized casters in my party, and counterspell is pretty much a given on any caster that could take it, because otherwise the casters of the party just roll over the encounter.)
- Make sure most encounters have some beefy bodyguards he can unload his magic missiles on, so even if his skeletons don't kill the main threat of the encounter, they still contribute.
- When he eventually starts counterspelling shield spells, have some low powered caster to counterspell the counterspell, and be well aware of counterspells limitation (60 foot range, must see the spell being cast)
This would work for me, because I tend to use a lot of spellcasters regardless. With the shield spell and fireball, they can stop the skeletons, until he can rebuild. I also love people considering these things, and really engaging in my game world. Can my skeletons use wands? is something every necromancer apprentice would ask his master I am sure.
Notice how I am taking care to give uses for the wands, without letting them break my game, if you are going to give every enemy and amulet of shielding, it is better to just disallow the wands to begin with.
This might not work for you, I run a high powered game, where both sides use a lot of powerful spells.
What you should do
It depends, consider these things:
- What will limit him from going all out 20 skeletons with 20 wands doing 60d4+20 damage per turn? It could be a simple talk with him, saying "I know it would make sense to go buy 20 wands, once you can afford it, but can we agree you don't hunt them down, and limit yourself to those found in treasure?", or maybe there simply is no way to find 20 such wands in a reasonable time. If it is only reasonable to find 2-3 wands of magic missile over his career in your world. It is not going to be a problem, and you probably don't even have to do anything to counter it.
- does the enemies you plan to use have access to the shield spell? Liches, Dragons, Wizards, Sorceress would all reasonably have access to the shield spell. But also high level fiends could get it added to their list. Be aware though, that enemies with shield over something like silent image are a lot tougher, so don't overdo this unless you think the party can handle it.
- How powerful is this character compared to the rest of the party already? We don't want him stealing the show. If he is powerful, consider asking him for help on tricks and build tips for the other characters, so they don't fall behind (Never let him dictate how the others play, only suggest).
If you are still on the fence, you can maybe do a compromised ruling:
Only skeletons who were spellcasters in life can use wands, and still only the non-attunement ones. This has no grounding in the rules, but the game has a DM for a reason, so that he can make rulings like this.
You can also say that only some wands work.
Skeletons cannot speak, you might say most wands use command words. This is explicitly against RAW though, but again, you are the DM.
Some magic items allow the user to cast a spell from the item, often by expending charges >from it. The spell is cast at the lowest possible spell and caster level, doesn’t expend >any of the user’s spell slots, and requires no components unless the item’s description >says otherwise.
You can even make it a quest.
You don't know how to make your skeletons use wands. But the legendary necromancer Bob Bonemaster, is famous for having done it. You can have the necromancer go on a quest to Bobs tomb and learn how he did in his research notes, or perhaps Bob is now an undead you can talk to, and convince to teach it. This approach is also good if you are a little worried the other players fall a little behind. Simply give the specific quests as well, that also gives them a boon of some sort.