Hello there, I am a Network Consultant with active CCIE Routing and Switching certificate, I provide such services for large scale and government sectors, I believe we can achieve your scenario smoothly with minimal or no interruption to services, however this will depend on the hardware you have, but there are many ways to change WAN IP's.
If we can have a quick chat I can give you in details how the shift to new IP addresses will be done as smooth as possible.