This is a full sheet of vellum i.e. a whole dried/stretched calfskin - well, trimmed, obviously, cows don't come that shape. It's hanging, and had been for a few hours by a single strip of Japanese tissue attached with starch paste - there's only about 3mm in contact with the vellum.
vellum.jpg
Regardless of value I would not pierce the visible area with a needle.
To simply float it you could either pass hinges through the mounting board or you could cut the shape out of the mounting board by hand, but slightly smaller, so it would not have to be a neat job. Then attach hinges to the perimeters of the piece, wrap them around that fall out and then fix it back in the hole it came out of.
To float it raised, cut that same shape out of foam board, hinge in the same way and then bond the foam board to the mounting board.
The type of hinge and adhesive I used on the vellum may or may not be suitable for your thing - maybe BEVA and hinges made from mount board surface paper would be better, without being able to touch and feel I wouldn't know.
This is not a conservation thing BTW - it's probably tourist junk like a Hong Kong oil (but I'd not poke a needle through the visible area of one of those either - I'd dry/wet mount it first) just a method that is effective, simple and invisible.
If it happens to also do no damage and is reversible you have my apologies 
