Utilizing NAT for an IP migration

I'm needing to readdress a production system we have. However, there are several 3rd parties that either point to this via IP or DNS.

What I'd like to do is utilize NAT to translate the old IP to the new IP. Both addresses are publics that I control the space on.

I'd like to remove IP a.a.a.a from this equipment. I'll be readdressing with b.b.b.b.

I'd like to then set up a NAT rule that forwards/translates anything from a.a.a.a to b.b.b.b. But if someone connects to b.b.b.b it goes untouched.

I set up a static translation. Pinging a.a.a.a responds with a.a.a.a, but if you ping b.b.b.b it says it was successful with a response from a.a.a.a. I just imagine this causing issues for anything TCP.

I'd appreciate any help or insight - I'm definitely not firing on all cylinders today.

I've tried the following

ip nat inside source static b.b.b.b a.a.a.a 

and

ip nat pool IP_MIGRATION a.a.a.a a.a.a.a netmask 255.255.255.252 ip nat inside destination list ip_migration_test pool IP_MIGRATION redundancy 1 mapping-id 100 ip access-list standard ip_migration_test permit b.b.b.b