You will probably need the third party to grab the natted address from a sent packet. Just getting the IP is probably not enough for an external source to initiate a connection in (if that is what you are wanting to do). The firewall will most likely remap the port number too, and unless the firewall is a promiscuous firewall, you won't be able to come back in from a different IP than the third part looking at your IP. It is far easier to punch out through a firewall to establish a connection to the outside world.
I did a lot of the networking stuff on FireWarrior, and NATs were the worst part, especially where there were two involved. NAT negotiation is possible but involves a third party to "guess" ports on port remapping for you and therefore isn't straight forward.