301 redirects are particularly useful in the following circumstances: (...) - You're merging two websites and want to make sure that links to outdated URLs are redirected to the correct pages.
As to when to execute the redirect, pending the redirect test of moving handful URLs not showing adverse effects, I would personally do it sooner rather than later. Otherwise your old site and new site are competing in SERPs and the new site could even be labelled as being duplicate content / content scraper (depending on how similar the pages are).
What is important is that the technical execution is flawless. It would also help if both sites are in the same WMT account although engine says the old site does not have WMT account. Unless there is a specific reason not to, I would verify the old site in the same WMT account with the new site (if the new site has one, or create WMT account if there isn't one) before implementing redirects.