Cherry picking applications for a backup
There is no straight-forward answer to your question without a full list of applications you're looking to migrate. 

Some applications that don't use installers, can easily be simply copied to an external drive and back again, and will continue to work just fine. 

Some applications that don't have installers, may ask for the license keys when you restore them because it for some reason has detected a change. 

However, you mention things like Photoshop and Office. Without a doubt there is no practical way of copying these to an external drive, "factory resetting" the laptop and put them back. These applications use complex installation processes that involve much more than just placing a .app in /Applications.

There might be ways to clean up the Mac though. Removing all other applications, removing configuration files you don't need with one of the many "app cleaners" on the App Store, removing unused user accounts, etc.