Step 1: Choose a Cool Tape
Step 2: Unscrew Case
Step 3: Remove Innards
It's both easier and cleaner to remove most of the internal parts with a pliers, twisting things until they break. You can remove everything with pliers except the one big fat screw boss in the lower center of the case.
Step 4: Tape Hinge
First, don't use tape that splits easily, like packing tape. Your hinge will die quickly. The best tape to use is gaffer's tape--it's both thin and flexible, and it'll never get any adhesive residue on your cards. Electrical tape is ok, but it's a little stiff, and can cause the case to spread. However, with a tape case this color, you'll never get gaffer's tape to match, so clear electrical tape can be used. Or you can just trim wrong-color tape cleanly.
Second, don't just tape straight over the top wall of the cassette. The tape will want to stay straight and will push the two halves of the cassette case apart from each other. Instead, fold a little seam in the tape above the joint, and make sure the tape doesn't stick that well to the top edge of the wall. That way when the cassette case is closed, the tape will push inward and let the case close all the way.
Step 5: Optional Additions
If the tape doesn't hold itself closed well enough from the friction of the screw bosses, you might glue in a couple (weak) magnets to act as a clasp.
If you want, you can cover up the little windows in the case so your cards aren't visible from the outside and so no dirt or gunk gets inside. I haven't found this to be necessary, personally.