move sites to other server

[cosmin]

I want to move some sites ti other server. All servers have cPanel and I want to move through this.

The problem:

I don't want to down this sites between dns propagation and lost e-mails.

My clients accept 2-3 hours of down for new IP propagation.
I can change the second ip from dns with the new second ip dns from the new server and wait few days to update the second ns for all domains? Work that?

Any ideea?