Step 6Ta-dah. Done
iImage Information

When glued, insert batteries and test it again. When the camera fires, pat yourself on the back for you have saved some money ($30 in my case) and hopefully learned something in the process.
Damn, it looks good. And it's smaller than the original remote. Ok, so it's been pointed out that it isn't actually smaller. I now make remotes into 2x4 LEGO blocks which is somewhat smaller than this here and uses surface mounted parts.
Now you can have fun photographing yourself or making super-steady tripod shots. It should be powerful enough to trigger even from 10 meters away with some aiming.