If you are changing hosts as well as registrar then:
Just don't cancel your old host until you have your site fully functional on your new host, then keep your old host for at least a few more days after you change the DNS settings. Users will slowly be directed to the new site as the DNS settings propagate out.
Only thing to watch out for is if you have any user registration or signup, disable that on the "old" site for a few days as you transfer over or you may "miss" folks as they get added to the "old" site's database or whatever.
Good Luck!