You forgot to told me which teaming load balance you're using on ESXi ? Anyway, if you aren't using the IP Hash, you can do the following:
1. connect the new switch to the old, using a trunk port (allowing all VLANs);
2. configure the ports on the new switch to support the connections from the old switch;
3. configure the VLAN interface (including the IP) but do not enable this interface;
4. move all ESXi uplinks to the new switch, try move one by one and verify connectivity between each move;
5. move all other connections from the old to new switch;
6. shutdown the VLAN interface on old switch and enable the VLAN interface on new switch.