When I install a new router I do the initial install with all network connections disconnected (physically or virtually since it’s proxmox). Once I get my IPs and ports set how I want I do the switcherydoo and disconnect the old one and connect the new one.
If you’re using the same subnet and your router has the same IP address the only down time should be the process of connecting devices, and maybe a bit for DHCP on your wan side. All internal devices should continue working fine, but expect their IPs to jump around as they get new DHCP leases.