So you have multiple public IP addresses? - One of which you want to use exclusively for the phone?
If the above is correct, think about this:
Put a switch in front of the linksys router (internet facing). The linksys router will get/use the same public IP. Assign another public IP to the phone (however you do that). All ports for the phone's public IP address will go to the phone. Now, not being knowledgable about these phones, I strongly suggest that you research the security ramifications of having them directly connected to the internet. I imagine that that would be fine, but what do I know.