Our recommendation is to fully prepare the new project, fix the URLs to make sure that you don't reduce your SEO score and then switch to the new project. This will provide the best experience for the site's visitors. For example, if the user navigates to one of the pages which redirect, he will end up in the old site. Any and all navigation links from there will probably keep him "stuck" in the old site which might not prove to be the best experience.
You could consider one of these options:
1. Create the new site on the new domain or sub domain while keeping the old one as-is until the new site is 100% ready.
2. The preferred way to do the redirects in this case would be with a custom HTTP module or using IIS to set up the redirects.
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