Personally i like to shower and shave right after, always found it very annoying that the mirror is always foggy even with the fan running, i even consider getting a more powerful
fan, i read somewhere to clean the mirror with shaving cream, i just happen to have in my travel bag a little sample can of Gillette foam. I put some in my hand rub it all over the mirror, wipe it all down with a cloth. After a nice hot shower Bingo clean mirror! 5 days later still clear!