Switching to a non-absorbent or less-absorbent wipe might help to reduce the amount of solvent that soaks in and renders the wipe ignitable. But, my guess is that this type of wipe will just smear and push the dirt around and not be very effective at cleaning. I also doubt that the wipe is your problem.
Both acetone and methanol have very low flash points. Switching to an alternative solvent will likely solve the ignitability problem, but it might not clean as well, will require extra wipes for drying, and will still generate a solvent-soaked waste. Abrasive blasting might be a viable way to clean the plate glass followed by air blasting and dry wiping to remove the dust. A switch to water-based glues, adhesives, and fluids might allow cleaning with water. An alcohol dip can be used for final drying.
You mentioned evaporation. Is this legal in the area? If so, the company might want to look into purchasing a drying cabinet to remove more of the acetone and methanol from the used wipes. The dryer can be vented to a thermal oxidizer or be equipped with a water scrubber if VOC control is required. It goes without saying that the dryer must be explosion-proof, that this arrangement will most likely be subject to a whole set of permitting issues, and it isn't pollution prevention.
Good luck on your search.
Mike Callahan, PE