Any firearm may be fitted with a recoil pad. On some, it is standard, but any good gunsmith will be able to fit you with a pad that suits you.
There are slip-on pads which have recoil absorbing sections with soft rubber “sleeves” which can be slipped onto any firearm. These are often used where the firearm would be compromised in value by removing a section of the stock; in order to keep the draw length right you need to remove approximately the thickness of the recoil pad from the stock.
Bob Allen is a manufacturer of fine clothing used specifically for skeet/trap shooting, and they make a fine lightweight jacket (and some nice shell vests) with a built in shoulder pad. This way, you have the protection but you don’t have to modify your shotgun, and the recoil is diostributed over an even larger area.
The old rule of thumb used to be, you held the pistol grip area of the stock in your hand and placed the butt in the crook of your elbow. If you could easily reach the trigger, the buttstock was the proper length. If the trigger was dramatically forward or back of your index finger, you needed to shorten or lengthen the stock.
In target shooting (rifles) or skeet/trap (shotguns) the number of rounds fired often necessitates a pad, or bruised shoulders often result.
For normal hunting use, the occasional shock of the gun against your shoulder is probably insufficient to cause you serious harm if you are in moderate physical condition.
In nearly 30 years of hunting, skeet/trap/target shooting, I can’t say I ever thought about, nor do I conciously remember, feeling recoil from a firearm. And I’ve shot some big rifles, like the 470 nitro express, which supposedly kicks like a mule. In shooting I tend to tune out all external annoyances so i can focus on the task at hand. I have come home after meets with bruises on my shoulder, but they didn’t last long nor were they unresonably painful.
But then, I’m a big guy, 330 lbs, and I love shooting so much I’d do it if It hurt like hell. YMMV
b.