AFAIK, there shouldn’t be downtime when changing the nameservers as long as you check that all your DNS records are correctly imported into CF during the setup process (I didn’t experience any when transferring my sites over to CF). You should set your records to 
rather than 
to start with and nothing should be affected. The nameserver change may take some time to propogate but should not cause your site to go offline. Once it is working with CF nameservers, you can start setting your records to and sort out any issues that may arise, e.g. mixed content etc. If you have any.
Again, as long as the MX records are correctly imported into CF and , your mail should still work OK.