How long a product takes to dry depends on 1) the product 2) the moisture content of the material it's applied to 3) moisture and temperature of the air, and 4) how it was applied.
So in other words, how long it takes is difficult if not impossible to answer. In general oil-based products take a lot longer than water-based.
I do have a simple test to recommend, though. When I'm letting a product dry I take a glass (real glass, not plastic) and turn it upside down on one of the treated surfaces. Then I sniff inside the glass every day and see if I can detect fumes. This is much more accurate than smelling the wood.
*********Disclaimer**********
Do not take a big sniff, especially the first day or so after using an oil-based product. This could be the ticket to a massive headache and hangover.
Another option is to take some cricket and toss them along with some vegetables into a coffee can. Poke several holes in the lid or cover the can with screen. Then place the can **lid side down** onto a treated surface after it has dried. Place some sort of spacer under the can so that some air can get into the holes.
If the crickets survive overnight (assuming it's warm enough to keep them alive) your cages should be safe for any herp.