I don't know what the minimum might be, but I can tell you what I did for my kids and what we use.

They normally shoot a ported, rifled 20 gauge with sabots for deer. But, this year I wanted them to be able to hunt with me during primitive season. So, I bought a used T/C Black diamond for a hundred bucks. I then took it into my shop and took about 3 1/2 inches or so off the barrel and recrowned it (most bp gun barrels are far too long and front heavy for a kid to use). Also took about an inch and a half off the stock. I put the original rear cushion back on and put a slip on limbsaver over the top so it has two on the back. Before I put it all back together, I took an old shot and put about 6 oz of lead shot in the buttstock. The gun is a tad heavy, but the balance point is exactly in the wrist. You can support the barrel with one finger.

We shoot 300 grain Hornady XTPs in front of 75 grains of 777. So far, they have killed two deer with the gun. Both at around 60 yards, both broadside and both through and through with great blood trails. With the extra weight of the gun, it more than shoves than kicks. At 100 yards it groups about 2 inches which is fine for them, I won't let them shoot much further than 75 yards or so. It is loud and has a wonderful ball of flame coming out the end, the kids love it. There are a couple of bp muzzies out there that havebarrels about this long. I have not put the load across a chrony, but it has performed very well on deer and kicks about like, or less than a 30-30.

Oh yea, while I am totally sold on shockwaves and use them exclusively in my Encore, I think with this lower powered load you would be better suited to use a Hornady XTP or similar hollowpoint sabot. I am not sure a shockwave would be at high enuff velocity to give you the terminal performance you want.

Good luck.
Hank