Hooks can & do dissolve in a fish's stomach, and they can also be "passed" if they're lucky enough to be in the correct position to do so.
You might try going up in size to a #4 hook, to dissuade smaller sunfish from swallowing the smaller hooks ... but, you're still not likely to keep them from grabbing the bait or nipping on it until they pull it off the hook. If you're fishing for Sunfish, try fishing deeper than where you're catching all these "runts". The bigger Sunfish will usually hold deeper than the dinks.
The hook release item you've pictured has instructions in this link : http://bakerhookout.com/portfolio/hookout-mini/
... cp