Officially, there's no way to do that. But unofficially, and completely unsupported, you could totally modify the AudioSets.json configuration file and have different sounds for different keys. See one of my responses in the previous comments for more info about doing that.
In the AudioSets.json file, look for "Bell Typewriter" and see how the specific key overrides are done for the Enter key. You could use that same means to override any other keyboard key. The names of the keys are listed here, but not all the rarer keys are available.
Just keep in mind that it is a completely unsupported and undocumented feature, and I'm not interested in spending time formally documenting the configuration file and answering further questions about it.