Okay, you do have a problem. I just rough-measured my Deerstalker; it's about 3.75 inches from the rear of the tang to the front of the breech plug (where it abuts the rear of the barrel) and the 57 sight sits right at the back of the tang. The mounting length on the 57 sight is almost 1.5 inches, which is the entire length of your tang. Even if you drilled/tapped your tang, the angle would be wrong. The 57 sight is angled to sit above the wrist of the Lyman rifles, whereas your tang appears to be parallel with the bore so the sight would be leaning forward.
I have seen a few rifles without a tang, but with a tang-type sight screwed to the wood of the pistol grip in the appropriate location. Far from ideal, but let's face it: this is not a long-range ultra-accurate gun. For the distances at which you will be shooting, this might be worth considering.
The other suggestion I have is to find an aperture sight that can be mounted in the existing dovetail on your barrel. Skinner sights makes one for the 10/22 which I have adapted for use in this way, and I have seen a couple of folding Williams sights that have an aperture in place of the notched blade. It works...but an aperture that far forward is nowhere near as quick to use as one back by your eye, so you'd have to consider this carefully.
Good luck with this project; unfortunately, it looks like a bit of a PITA.