Beautiful animal—incredible variety of colors!
Can you elucidate on why the enclosure cannot be moved? IMO, that would really be the best way to relocate him.
Zero VOC paints don't have VOCs, but that doesn't necessarily mean they don't have fumes. I've used some latex paints that were as close to odorless as one might imagine, and I've used others that you could definitely smell.
I can't say those fumes are harmful—IDK. I can only say if it were me, I would relocate the enclosure to as far away—and in a separate sealable room—as possible, seal off any registers & returns in the room to be painted, towel under the door, open its windows if outdoor temps are within those recommended for the paint, and allow 24-48 hrs. for any fumes to air out. Paint drys faster than that (usually ½ hr) but takes longer to completely off-gas (I've had rooms take up to a month to off-gas completely—until you can't smell fresh paint anymore).