Piece of cake.
You hook the computer up to the router by either a serial "roll-over" cable or start a telnet session to the router. Type in the configuration commands and disconnect it.
You have a configured router, and no logs or traces left on the computer.
So, you DO have to use the computer for the configuration, but you don't have to leave a trail.
Your PC wouldn't leave a trace log of a telnet session?