Migrating from Postgres RDS to Aurora without changing endpoint

I have around 40 micro services that connect to my Postgres RDS database. Now I am considering migrating to Amazon Aurora. Each of the connections connect to the RDS endpoint and modifying that across 40 micro services will mean that there will be quite significant downtime, coordination and stress. I am assuming that there would be a smarter way to do this, where I can somehow keep the endpoint and just redirect it from RDS to Aurora. I have looked into Amazon RDS Proxy, and it would be great to change all the micro services to use that as an endpoint, but it seems like I am adding a lot of complexity for this small purpose.

Researching this did not get me far, which makes me believe that I am missing something obvious, but I don't understand what it is.