Strictly, a feebleminded creature can't activate a wand
Wands on Activation says, in part, that
Wands use the spell trigger activation method, so casting a spell from a wand is usually a standard action that doesn't provoke attacks of opportunity.… To activate a wand, a character must hold it in hand… and point it in the general direction of the target or area.
(Emphasis mine.) So, while exceptional rules surround it, casting a spell from a wand nonetheless remains, technically, casting a spell, and a creature affected by the spell feeblemind "is unable… to cast spells." However, such a ruling does complicate the rules a bit, reverberating throughout the system and raising additional question, so it's possible the GM may, instead, consider the following:
Can the feebleminded creature wave a stick and speak a word?
To review, to activate a wand, in addition to the creature having the spell on its spell list, the creature must hold the wand in an appendage, point the wand in the general direction where the wand's effect will occur, and—as a wand is a spell trigger activated magic item—speak the single word that activates the wand.
With this in mind, a creature that possesses a spell list and that's still anatomically capable of A) holding a stick, B) waving a stick, and C) forming words—even if the creature doesn't know what those words mean—possibly can be trained to activate a wand even if the creature's affected by the spell feeblemind.
That is, while the spell's effect prevents the creature from casting spells and causes the "creature's Intelligence and Charisma ability score each [to] drop to 1" and renders the creature "unable to understand language… or communicate coherently," the affected creature is not rendered wholly mute nor does the spell render the creature anatomically incapable of speech. (At least, this GM assumes the spell doesn't change the creature's anatomy, the spell not saying it does. By the way, anatomy is, for example, what prevents an at-least-Intelligence 3 animal from speaking—yet not learning or understanding—a language via, for example, the skill Linguistics; more on that here.)
The Handle Animal skill says, "You can use this skill on a creature with an Intelligence score of 1 or 2 that is not an animal, but the DC of any such check increases by 5," so this GM suggests that an ally that wants such a creature to activate a wand make a Handle Animal skill check to push the creature to perform a trick it doesn't know (DC 30), the trick Activate Wand. (Such a trick is obviously so uncommon as to go unmentioned by the Handle Animal skill's list of Common Tricks.) This GM also suggests that if the ally wants to actually train the creature to perform the trick Activate Wand upon being successfully handled that such training takes 1 week and requires the ally succeed on a Handle Animal skill check (DC maybe 25 but in this non-animal case 30? Ask the GM). This player urges using for training purposes, for example, a wand of virtue instead of, like, a wand of fireball. (It's the GM's call as to whether each wand is a different trick, but keep in mind that, as per the skill Handle Animal, an Intelligence 1 creature has "the same limit on tricks known as animals do.")
The GM may dodge even this workaround by ruling that the creature affected by the spell feeblemind can't even "understand speech" as a concept (limiting the already burdensome creature to instinctual barks, growls, and whines in response to real or imagined stimuli), therefore the creature can't "communicate coherently" with the wand. While such a ruling seems strained to this GM, this player wouldn't abandon a campaign over it.