There is probably some convoluted script that can be written to do this, but sounds like it would be simpler for your client to just put in the right WANIP into the RDP application LOL.
Why not setup the WANIP as a dydndns type address with a provider and have their service switch to the new WANIP if the primary is down and that way you simply program in the domain name of the dyndns that is setup, as a route rule for RDP traffic for example, and thus transparent to the end user.