As far as I know, a forced update like this is not directly possible. You might be able to reduce the DNS downtime by reducing the TTL (Time-To-Live) value of the entries before changing them, if your name server service provider allows that.
Here’s a guide for less painful DNS changes.
A fair warning, though – not all name servers between your client and the authoritative (origin) name server will enforce your TTL, they might have their own caching time.