I have Silhouette Studio and Design Studio on my MacBook Air but am unable to access it. I get a message saying the developer needs to update it. How can this be fixed?

This message means exactly what it says. You need to contact the app's developer to find out if they have a version of their software that will run on your notebook's macOS version.

Ref: Contact a third-party vendor - Apple Support

Have you recently upgraded to a later, 64 bit-only, version of MacOS? If so, you need 64 bit Adobe products. Obviously this is just a guess.