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Welcome to TFL !
The Skinner's definitely the best size/fit for a scope-grooved .22 levergun, including most Henry's, but (like ALL groove mounted peep sights) will require a front sight that's taller than issue, in order to zero the rifle. (which can be an issue for some folks on the H001 Standard)
All other things being equal, no one receiver peep sight is any more/less accurate than any other - it's all on the shooter to use one properly (look through the aperture w/o seeing it & focus on the front sight & target).
FWIW - with any receiver peep sight installation, I would heartily recommend replacing the existing rear bbl open/iron sight with a slot filler blank, to afford oneself a clean/uncluttered sight picture.
BTW - If you're considering the "peep" sight that resides in place of the rear bbl open/iron sight, IMHO those types of "peep" sights (a few others make them, also) are too far from a shooter's eye for fast/effective use (aka: best practice).
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