yes live migration needs shared storage, so "connection" is required.
if you could use external storage for the vm, you could stop the vm on pve 2, then
disconnect external storage from pve 2 and connect the storage to pve 3
if storage & all network, etc setup is identical between pve 2 & 3, move vm config file to pve 3 (same VMID), restart the same vm from the same storage. It could take a few minutes.
I'm not sure but it could work. Try with a smaller test vm before...
Marco