Certifying New Versions of SQL Server
Answers originally left as comments

I think you identified it in your question, regression testing. You maybe able to thin down the testing to just corner cases of the functionality. However if you are looking at more than “does it run” and wanting to test “how well does this run” a full test maybe your best option. – Aaron

To me, this is less of a question about the database, and more of an issue with your regression testing. You may want to explore ways to make your regression testing less labor intensive. – AMtwo

Also there aren’t that many things that work in 2008 and break in newer versions; the exceptions are limited to lists documented on Microsoft’s site, like this one for SQL Server 2016. So outside of those items, you should generally expect that moving to a new version should just work. Performance testing is something completely different, of course, and there aren’t any magic shortcuts aside from testing. Baselines are a good start. – Aaron Bertrand