DNS pointing question - Temporary moving webserver to another site

[Uzee]

Hi,
We have a peculiar need which is temporary but necessary.
Our main website is say, www.oursite.example.com, where www is just a cname pointing to our webserver and we run authoritative nameservers for the zone oursite.example.com. Our webserver IP is say, 10.11.12.13

Now due to an unavoidable outage we need to temporarily move our site to another location for 1-2 days. This other location is auhtoritative for example.com but not oursite.example.com. The new webserver say webserver2 will also have a different IP, like 15.16.17.18. We can clone the webserver quite easily but the question arises, how will we be able to point the cname to this other location since in order to lookup www.oursite.example.com, any request will need to talk to our nameserver which will be unavailable. 

Any ideas if this can be done... and how?

uzee