I use stain and Helmsman sealer and there are no problems. If the chams licked it there wouldnt be any problem as well, they would hav eto eat paint chips and ingest it for complications. You had better seal that would very very well or its going to be a big waste of money. This is assuming you are misting often, as you should anyway.
There are great products out there, get one that is for outdoor use for like park benches or exterior dorrs ect. It is UV resistant and weather proof, all of which you will need for it to not look like hell in 5 months. The cham isnt going to lick a piece of vertical wood in the first place, but if he did and the stuff is dry there is no harm done.
After you sela it let the cage sit for about 3-4 days to air out, it will smell fresh so you need to get that smell out.