Perhaps try shrink wrap bags and mount with double stick strips? (I never tried it, hence the question mark. Jewish party goods stores carry them for mishloach manos.)
Or if you are ready to spend try finding a water proof shadow/display box. Or perhaps you can caulk and seal the gaps of a regular wall-mountable display box. Make sure the depth is enough for your stars. If you use a “shlock” you might not even need to seal it, but of course that’s your call.