A lot depends on the thickness of the coating. Yacht varnishes are normally touch dry in 4-6 hours, and through dry in about 24. It depends a lot on the brand and which resin/carrier solvent they use.
Most varnishes these days are quite 'user friendly' i.e. less harmful solvents and driers. I'd read the label on the back and avoid anything containing Xylene, toluene, cobalt driers or MEKO (methyl ethyl ketoxime).
Not had any experience of the above in relation to herps, but they aren't very nice chemicals!! If you look for one with a 'Low VOC' rating, that will mean that it is probably water based, which may be preferable??
I'd give it at least 24hrs after any noticeable odour has gone before putting anything in there - ideally a lot longer. Personally, given the option, I'd give it a week or so to dry (with the heat on as Gaz said) to be absolutely sure.