Waxing your cool little item should not remove any of the paint , K_B .
There may be loose paint near the edges/margins of the still-painted areas , but it may be knocked off by simply brushing it (not so likely) ... but if so , it's loose & is gonna fall off anyways .
The main idea here is to stop/arrest the current oxydation on your item via sealing it off from the atmosphere (& give it a better/more uniform appearance) .
A paste wax , such as what would be used for furniture (Johnson&Johnsons , etc.) , will do the job .... but don't use 'car wax' .
Some would suggest that you could use black shoe polish (paste-type) or stove-black as well ...plain old paste wax works well enough , though , & has no pigment .