Putting on my devops hat: as long as both old and new DNS servers are properly authoritative for the domain for at least as long as the TTL (insert furious waving of hands here), there shouldn't be any downtime. If you're literally taking one down and standing the other up....yeah, that's downtime.
(Lots of detail elided because while I can see you're currently using Cloudfront for public DNS, I have no idea whether they're truly authoritative or slaving from a hidden master, if you're outright killing the cloudfront account, etc, etc, etc. Nobody likes a backseat driver, you probably know all this already, etc. Have fun.
)
You probably know this, but maybe as general advice for future readers: lower the TTL as much as possible as early as possible before the move, then bump it back up (on the new host) afterward; if there's an outage window, it'll minimize downtime for well-behaved (*) clients.
(*) there are no well-behaved clients