One of the sites I support is moving to a new host and a new redesign next week.

The current site has been running a Google Custom Search Engine, and will be on the redesigned site. 

The old/current site is going to be moved to a sub-domain for archival purposes: archives.mywebsite.com, and that'll need to be indexed going forward as well.

The question is how to handle the cutover.

Do I have to do anything specific in regards to telling Google to use the 'new' site index instead of the old?

Do I have to go into Google Webmaster Tools and re-verify mywebsite.com and archives.mywebsite.com?

Thanks in advance!