.... or you can keep the same 8333 port on that computer and set up your router to forward a different port number on the router to port 8333 on the computer.
I am not sure that would work. A full node broadcasts the port it uses, so the node needs to know its global internet port. Having the router remap the port will mean that nobody will be able to connect to the 2nd node, since it will claim to use port 8333.