I think you do need to have the spell on your list and capable of casting it and here is why.
Wand of Magic Missiles (from the starter set)
This wand has 7 charges. With the wand in hand , you can use your action to fire the magic missile spell from the wand no components required and expend 1 to 3 of the wand's charges. For each charge you expend beyond 1, the spell's level increases by 1.You can use this wand even if you are incapable of casting spells.
The wand regains 1d6 + 1 expended charges each day at dawn.If you expend the wand 's last charge, roll a d20. On a 1, the wand crumbles into ash and is destroyed.
Wand of Magic Missiles (from the basic rules)
Wand, uncommon
While you hold this wand, you can use an action to expend 1 to 3 of its 7 charges to cast the magic missile spell without using any components. For 1 charge, you cast the spell as if you used a 1st-level spell slot, and you increase the spell slot level by one for each additional charge you spend.
The wand regains 1d6 + 1 expended charges each day at dawn. However, if you expend the wand’s last
charge, roll a d20. On a 1, the wand crumbles to ashes and is destroyed.
So they changed the wording from fire the magic missile to cast the magic missile spell, and removed the sentence about using it even if you are incapable of casting spells. So if they made those changes I would say the intent is to have as a caster only device.
But the basic rules also say
"Work in Progress!"
This information from the Dungeon Master’s Guide represents in-progress versions of the rules in that book. Updated information will appear in future versions of the D&D basic rules.