Is it safe to make a Unique Index the Primary Key?
No it's not safe.

From a query perspective it might look OK, but if you don't know how the application handles primary keys you shouldn't change that without checking with the vendor first.

You could break their error handling, their future update scripts etc.

Just to give you an example, during a future upgrade they may want to change some tables where you added CDC and they will receive an error. What does your contract say about support in that case?

If you are using a vendor database it's up to them to support it. If you go around making changes you are basically putting your system in a state they never tested so they would (rightfully so) probably tell you you have an unsupported configuration when things go wrong.

We don't know what application or vendor you are talking about, but if it doesn't support customizations you probably shouldn't customize the database without asking them first.