Hi Magpi
What about wood? and glass.
When I was A kid I contributed my fair share of fingerprints leaning over wood bound display cases at the science museum. Come to think of it I still do it!
Get some 20 x 20 hardwood and cut a corner out making it into 20 x 6mm angle with a router or on the saw bench then round the edges that will not touch the glass, you will need to make a jig, then mitre the pieces to make a frame. cut to size glass is not that expensive.
You will need a rebated base and a thicker mould around the bottom edge, you will also need some 6mm or thereabouts quarter round for the inside corners of your case. You may be able to get the materials ready made from a specialist timber boulder. and a tube of silicone or some epoxy to glue it all together.
A little French polish and the job is done.
You will need a rag the fingerprints that visitors leave as they are in awe of your work.
Regards
John