Solvents tend to be flammable - after cleaning with a solvent, I would let them air dry fully before using a hair dryer.
Re James' suggestion of sticking them between the pages of a phone book to absorb the solvent - but when was the last time you saw a phone book?
In the old days, one of the options for drying photographic prints was to place them between blotters to dry. However, the concern was that if a print was not fully washed, the chemicals in the print would contaminate the blotters, which would then contaminate other prints. When I was doing darkroom photography, I always air-dried my prints on fiberglass screens that I could wash to eliminate any contamination.
I could also see a situation where the solvent used to clean the adhesive off the stamps might 'lift' the printing on the page of the phone book. That;'s also a risk with newspaper - if the ink can come off on your hands while reading the paper, it could also be transferred from the paper to the stamp.
In fact, there is a technique for transferring photocopied images to things like wood that involves placing the image in close contact with the wood, and then soaking it it a solvent (acetone) that releases the bond between the powder that makes up the photocopied image and the paper.
So - my conclusion is that if a solvent is used, it would be best to let the solvent evaporate directly into air. It could be potentially conterproductive to put solvent-soaked stamps in contact with anything else until that solvent evaporates.