No glass is a no-no. Oils on paper are usually preliminary sketches for the real work or simply too-mean-to-buy-a-canvas works. In any case they are going to be very fragile. They generally aren't intended to last.
Oils on canvas can withstand repeated patching and re-painting. Paper can't be treated in the same way so it has to be protected. One sharp poke will destroy it irrevocably. Plus cleaning it in the same way as an oil on canvas would be problematic if not impossible.
Also, the oils in the paint will have penetrated though the paper - even if it was primed. The paper would have soaked up the oil in the paint like a sponge, which would weaken the bond. Bits are going to flake off as it ages.
This rules out using any type of glue to mount it to a board. It won't stick evenly. Framing it like any other work on paper is the only satisfactory option. And I would use Mylar edge supports rather than hinges.
Whether you go with the customers wants is up to you, but be sure to impress upon him the likely consequences.
