Hi there,
I am actually in the exact same situation as you are in for 2 of my clients, but they are doing a re-design not for conversion issues, but just updating the site and moving it to a cms.
I got the client to map out all the new pages so we can put all 301 redirects in place, especially for pages that will no longer exist, we make sure we point them to the right category page.
Also we try to contact as much of the webmasters from where we have links from as possible to point the links to the new url, because you don't want your links to lose value due to redirects.
Keep an eye on Google WMT after you made the migration to make sure no errors come out I guess, I don't see much issues with site migration if you can keep urls the same but you never know.