I was wondering if this can be done? For example, if a browser session is always run in the same sandbox, would it be possible to delete the whole contents when the browser is shut down, but *keep* e.g. the cookies file *without* restoring it? Just have it remain in the sandbox and delete all the other files from it?

Oh, I meant to say "automatically" - obviously it can be done manually, but I was wondering if Sandboxie could be set to keep some files in the sandbox when the option to delete that sandbox's contents after shutting down is selected.

No, there is no Sandboxie setting for this.

You could achieve it by using an external/specialized application for deleting the sandbox contents; you could write your own script or whatever for this. Read this