Thank you, Tiny11 looks like exactly the thing!
I didn't know about the manifest thing but that looks like almost what I need. It'd allow me to at least tell the user what itch downloaded is an installer, but it still seems janky to stick an installer in their start menu (as I understand itch does with downloaded exes, matter what the manifest says? I think? It's not clear from the docs).
Is there truly no way to make itch understand that an .exe file I've published is an installer, and not the game itself? Alternatively, is there truly no way to tell itch what file associations to make for my app?