I see. In that case, I’m guessing the greetd file contains something like auth include system-auth and the system-auth file has the pam_fprintd.so line? If that is the case, then you could probably work around the problem by making a copy of system-auth (e.g. cp system-auth my-system-auth) and then changing the auth line in your greetd file to auth include my-system-auth.
Be sure to have a root session open somewhere while you are editing and testing because you could lock yourself out if you misconfigure these files. (Also, it is a good idea to make sure they don’t work when they are not supposed to.)
Edit: authselect probably just does an all-or-nothing configuration. Since you want something more complex (works with sudo, but not with greetd) you will probably have to edit the PAM conf files manually to achieve that.