Don't feel knocked up or out of place. Even the NOS mirrors in the box come with the entire assembly bolted together. I've never taken one apart, but there's got to be a way to do it. There's no possible way that I'm currently aware of to get the thing apart without busting the glass. Even then if you have to reach screws back there, you could carefully drill holes where needed on the plastic glass backing. The holes would be hidden by the new glass I would imagine.
FYI, they do make aftermarket mirror glass replacements if you break yours. A few dabs of urethane glass adhesive should do the trick. For non-wedge sport mirrors, Burco makes them under p/n 2135 (driver) and 33183 (pass.). They're USA made, btw. That's why I would go with them if an NOS restoration wasn't required. I say that because they etch their a tiny burco "b" and part number on the bottoms of them.
If you happen to run across GM glass, here's the part numbers you would need. Long discontinued, but when these things were all over ebay for $5-10 a pop, I would snarf them up when/where I could. Although I didn't even pay attention to the wedge glass. Should have, but didn't. RPO D35 - sport mirrors driver remote, pass. manual. RPO D8- sport mirrors driver AND passenger remote. Glass fits either type. They don't fit any of the chrome factory mirrors.
For non-wedge style mirrors (RPO D35, D68):
9606230 for driver side
20210902 for passenger side (convex)
For the Corvette, F-body, and 86-88 Monte Sport wedge mirrors (RPO D35, D68):
20318502 for driver side
20289778 for passenger side (convex)
Unsurprisingly, you can still dig up a few GM wedge mirror glasses.
