It would only work for records off the root domain, so it's a little kludgy. You'd have to configure the MX records on the current DNS servers to point to the new mail server address manually, and you'd probably want to have a redirect setup on the local webserver to redirect domain.tld to www.domain.tld. Once that is done, you just need to reference the records to move over like this in the zone file:
Basicaly you are treating each record as a new subdomain and delegating the authority to the new name servers.
By far the cleaner approach would be to make the existing servers slaves of the new servers for that zone. It's only about 5 lines of configuration on named.conf on the new and old servers. Basically you just need to change from type master to type slave on the existing servers, define the new servers to be masters, and make sure you allow transfers on the new servers from the previous servers. You can find all kinds of applicable documentation here: