I don't think that you do require an additional 'box' to go in-between.
As I understand it, what appears to be an ordinary Ethernet port on your HP printer is actually an integrated HP Print Server.
In theory, therefore, all you need to do is configure this as necessary. All they basically require is an IP address and netmask. I've never used one with DHCP but I am sure that's a possibility.
Does that sound about right from the printer manual ?