I played around with this a few years ago due to a neck injury. Tried several different wads with SR7625. The loads using Claybuster's Lightning wad were noticably softer on the shoulder. I later called Claybuster and they agreed the lightning wad was the softest shooter in their lineup.
That Lightning wad (CB4100) can cover a broad spectrum of uses. Although it is marketed as a 7/8 or 1-ounce wad, its shot cup is the same depth as a 1-1/8 wad. And it seals well in straight-wall hulls as well as tapered ones. You have to be careful using it with heavy charges of high-density powders, as it is longer than a typical 1-1/8 wad. I had a informative telephone conversation a few years ago with the founder and then-owner of Claybuster Wads during which he told me that it was his favorite and most-used wad of their entire line.
While some powders may have recoil that is less sharp I agree with Timb99 actual felt recoil is a matter of physics and if you want to lessen it you should consider a recoil reducer or automatic which mechanically dampens recoil.Jerry