Not certain which type of sensor it uses, but in any case painting it wouldn't fix it. The problem with a scratch is now it will register that as a fingerprint ridge, but it is in a fixed location, so theoretically if you re-register your finger on the scanner and always position your finger in *exactly* the same space it would still work, but as soon as your finger moves slightly, the scratches position relative to your fingerprint changes, thus changing the fingerprint that is read. You would have to fill the scratch with the same material that it is coated with, provided the scratch is just in the coating, and it isn't say a capacitive type which you've scratched part of that capacitive coating. Thus for a home-repair likely out of luck I'd think.

I could be wrong, any hardware guys please feel free to chime in over me.

Note: slightly simplified explanation but mostly holds for the three common types of sensors.

You could make an attempts using a scratch remover, which are available for scratched screens. There is some chance that it gets you there, though it depends on too many unknown variables to know for sure.

What about sanding it down, then..? This way it won't be a ridge anymore