If the customer wants to spend the money to frame it, he/she probably expects to enjoy it for a long time, so I would not want to frame it without glazing. I would recommend 98% or better UV filtering glass or acrylic, and a spacer to avoid abrasion at the high spots.
I would also suggest permanent mounting to a sturdy substrate of foam board, GatorFoam, or fluted polypropylene. Dry mounting to a pre-adhesive board, such as Kool Tack, works well. Chemistry in the frame is not much of an issue, IMO, since the composition of the puzzle itself probably is more invasive than everything else in the package.