I can tell you with 100% confidence that the way we set it up, nothing would EVER snap back at the user. There isn't recoil. We have launched hundreds of kids with the same setup and people just simply don't get hurt with it. It is, dare I say, fool proof.
You have a carabiner on the haul rope, you have a carabiner on the swinger's harness. Clip the static eye of the snap shackle to the swinger's carabiner. Clip the opening eye of the shackle to the haul rope carabiner. Haul swinger in place, they pull the pull cord, let the fun ensue!
The HH is an amazing tool, but it's kinda hefty for this, no? Couldn't it slam down into someones knee or something like that?
Here's the snap shackle we used-
I swapped the pull cord for one that I made with a larger monkey's fist in it. Worked sharp.
Your system has the advantage of consisting of pieces you already have.
I use this snap shackle on my big shot, too. It's gentle- it doesn't recoil back at my hands.