In your encoder settings, set one of the IPs. In your Player, such as flash, or your web server, set the other IP. You can also take a look at VHhost.conf, where you can specify an IP address for Wowza to listen on certain ports. So, you can bind port 1936 to one IP, and publish to that IP. And bind 1935 to the other IP, (the one you give to clients).
If you're using a .stream file to pull a stream into Wowza, I think, that the network interface chose will be determined by your OS/routing tables. So, you could setup a route something like this: