For the mentioned reason, I'd go the safe way about toxicity in a music instrument.
The choice is huge, and I only mentioned a few ones, because there are so many plastics. Within each basic composition (PE, PA...) you have variants depending on the molecular mass, the way it was produced, the additives... These variants are distinguished by trademarks which depend on each producer. That's the common life of every plastic buyer.
http://en.wikipedia.org/wiki/ThermoplasticSome plastics are legally allowed to contain food. This would be the (exaggerated!) safe option. They include PE, PP, PET, PETP and more - though PET is meant to be injected, I doubt you find it as thick plates.
I wouldn't take PTFE (Teflon is one trademark), because it's mechanically so weak. It creeps over time. And it's so expensive. Worse, its fumes are toxic, and fast rotating hand tools can produce them.
I'd would take no PA nor PVC in a humid environment.
Here they explain the most common PC contains bisphenol-A
http://en.wikipedia.org/wiki/Poly%28methyl_methacrylate%29whose danger is uncertain but may give a bad image of your product in the future.
This would leave PMMA as the only really transparent option. Easy to saw, file as well. But I don't like PMMA too much, as I felt its fumes made me cough after processing it with hand tools.
Do NOT use any resin you cast by yourself. You would always leave some unhealthy monomer and catalyst in it.
Don't heat-process (hot bend, weld etc) any functionalized plastic, as this would create new small molecules. Only PE and PP then.
Don't use any glue (and certainly not MMA!).
Nice, I just read that some POM have been approved for food contact
http://en.wikipedia.org/wiki/Polyoxymethylenethis is the one plastic for mechanical engineering. Strong, easy to process. Not transparent, but can be any colour.
Edit: susceptible to cracking by HCl, and breathe contains some. Oops.
Ask for the experience of flute makers.
Here they suggest some possible toxicity of PET should be investigated, that's new to me
http://en.wikipedia.org/wiki/Polyethylene_terephthalate"PMMA has a good degree of compatibility with human tissue" they say
http://en.wikipedia.org/wiki/Poly%28methyl_methacrylate%29#Usesthis would make it better than PE and PP which are harder to saw and file
I'd suggest that you find
samples of PE, PP, PET, PMMA, POM and
try to process them by yourself: differences are big. And check their Material Safety Data Sheets, yes - of the very precise material you plan to use: the exact trademark of the exact producer.