If the STC applicable to a propeller (or any mod) is appropriately installed on your plane, you can replace the same product (the prop). Think of the STC as a expansion to the type certificate for you plane to include the added change. The STC can only become invalid by AD, or unavailability of the mod part - which does happen. Note that for an STC to be valid on your serial number plane, you may require evidence that the STC was sold to you specific plane - some STC's come with a permission letter, or your registration on the copy of the certificate with the word "only". This is so the STC holder cat contact the airplane owner in the case of a problem - which also happens, I'm dealing with one now for a client.
Any other propeller change you desire for a GA plane will be in one of two categories: The is an STC already you can buy, or, don't bother. Noise compliance requirements have made prop approvals very complex and costly. I used to approve many such changes in Canada by serialized STC, but it's a problem now that noise is in the forefront of regulator thinking. I have done an EASA compliant niose test for an MT prop installation - it was a big deal!
Find a prop which is Type certificate or STC approved on your type, that's what to use.