I am using Sharepoint Online and Office 365, and I would like to be able to choose which document libraries show up in desktop applications (e.g. Word or Excel) when saving files. I feel pretty certain this is somehow possible, as for example, in the site contents of my site, there are Site Assets and Style Library document libraries. These document libraries do not show up when trying to save a document in Word. In this example, I'd like to be able to hide the Test Wiki page library and the document libraries associated with Shortpoint (which are already hidden in the browser, so they do not show up in Site Contents already). Is this possible?
No, it cannot be removed/hidden.
You can remove
Add Items and
Edit Items permissions from the users in the specific libraries, for example give users
Read permission or less in these libraries, so that they cannot upload the files to these libraries from Office client applications.