Tapping out the old one is not a problem, as it will get tossed afterward. It's not recommended tapping on the new one, though, as it can brinnel the races and lead to early bearing failure. It may be possible to press it back on with the vice...maybe. Depends on how tight the interference fit is.
A lot of auto parts stores rent the bearing removers. They look like a midevil guillotine with 2 long bolts that close the blades together and slice the bearing off the sleeve. They often take a press to finish pulling the bearing off, though.
For $99 direct from China and to your nearest Northern Tool...a cheapo press sure comes in handy for a lot of odd bearing jobs. The saddest part is the bearing remover costs more than a cheap press!?!