With the Eagle Auto Router, how can I route all signals expect for ground airwires?
If I draw the ground polygon first, and then auto route, none of the signal air wires get routed


That is the problem you should be solving (and/or asking about). If you draw a ground plane your ground wires should get routed. This suggest there is something wrong with your ground plane.

Also routing the ground wires as last is a bad routing strategy. You want to have excellent ground. I would prefer to route my ground first!

(By the way great example of an xy-problem.)