Impact of changing VLAN on hosts

I think I already know the answer to this but thought I’d double check with the community here as there are others better experienced than myself.

I’m looking to change the VLAN ID used for management/VM traffic on two separate clusters.

The hosts in these clusters are connected to 2x layer 3 core switches where the VLAN SVIs sit. The ports connected to these hosts are trunk ports.

Currently VLAN 1 which is untagged is used for host management and VM traffic for the main production servers.

As a recommended network security practice to move off VLAN 1 we are wanting to change this to another VLAN ID but keep the same SVI address. (I will be addressing separating host/vcenter management traffic later)

My plan is to create the new VLAN ID/interface on the core switches then remove the VLAN 1 SVI address and apply this SVI address to the new VLAN interface.

After this is done I will then change the native VLAN on the trunk ports going to these hosts to the newly created VLAN ID.

Is there likely to be any impact during this change over? My initial thoughts are that this may briefly impact traffic to and from other VLANs as the gateway address will be unreachable for a short period of time.

Is there a better way of doing this with impacting connectivity? Obviously we would do this during a maintenance window.