You have 2 options
1) As discussed connect the WAN link, the pix outside interface and a router interface to a new switch and give the router the spare address from your pool.
This should work fine with incoming traffic but it is the return traffic you may have an issue with.
This depends on your topology but what is the default-gateway for most of your internal clients - is it the pix inside interface ?. If it is what model of pix and what version of software ?
Are you proposing to connect another interface on the router to the inside switch ?
2) Have the router connected to the inside switch and allow the GRE traffic through the pix. You would need to NAT the router interface to the spare IP address on the Pix.
Again return traffic is the issue.
So could you elaborate on how you envisage the routing happening for traffic returning back down the GRE tunnel.
Note that if you have an internal router that is the default-gateway for all your clients then it becomes a lot easier.