Remotely change uplink SVI?

Hello,

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Is it possible to remotely change an uplink SVI? For example, A router (interface g0/0, ip address 10.10.10.1 /24) is connected to a switch (int g0/24 VLAN 5) and the switch has a management IP of 10.10.10.2 /24 on int VLAN 5 with a default route pointing back to 10.10.10.1.

How can I move 10.10.10.2 from VLAN 5 to VLAN 3 without having physical access to the router (console access)? I have SSH access but I'm afraid once I make any changes, I'll lose the SSH connection.