The VMAX are the most stable Storage environment on the market so dont worry about them
Yes all you need to do is stop the EV services, Mount the new LUNS to the EV servers and copy data from one to the other. Dismount the old LUNS and change the drive letter of the new LUNS to the same drive letter as before so what was drive F on the old will now be the new LUN mounted as drive F
Make sure you set the folder view to display hidden files to ensure you miss nothing when you are copying.
Once the new disk is populated and renamed reboot the servers.
Another way to do the copy is if you you do a LUN copy through VMAX this will only work if both old and new storage are part of the same FC domain. It will speed up the copy because you are not using the OS to copy you use the FC to copy LUN to LUN