OK, let’s see if I can contribute to moving this a step forward.
McMaster also sells part number 8574K26, which is a 12” X 12” piece of 1/8” thick clear polycarbonate sheet for $5.78. This would be enough to cap several tubes. You’d have to be able to cut it to shape, of course.
As to glue, I found a site that states that cyanoacrylate (also known as Superglue) will bond to polycarbonate. No problem there. Cyanoacrylate glues are readily available and not expensive. You might want to get the cyanoacrylate gel to make it easier to work with.
If I’m reading the information right about part number 5012K29, the Acetal Quick-Disconnect Tube Coupling Socket, 1/4” NPT Male, 1/8” Coupler, Shut-Off, this is what McMaster calls a panel-mount socket and plug or a bulkhead coupling. They say you would need an 11/16” diameter hole to mount the 1/4” coupler size. Note that this is a THREADED fitting, so I don’t know how you get the 11/16” hole threaded. I’m sure there are threading tools around, or perhaps you could just glue it in place.
You would still need some technique to smooth off the tube edges for the end that contacts your body.