I'm fortunate in not having any shoulder issues (hex hex, jinx jinx) so I've never even thought about my shoulders relative to SUP until you asked, so IMO shoulders and SUP get along well.
SUP works the core first and foremost, legs second, arms a distant third.
Yeah so well I just bought an inflatable board, my first inflatable. I launched it on a beach at the Sound and due to a strong off shore breeze, I decided to go up a nearby long and winding tidal creek to duck the wind.
It was utterly awesome.
I'm a big fan of doing low key mini adventures instead of spending time and big money to do bigger, splashier trips, like running the Colorado river through the Grand Canyon. Hey that trip would be insanely cool, duh, but short of that, plenty of good times to be found close to home wherever you live, imo.
After merely one trip, but also a lot of online reading, I believe an inflatable is a total no brainer for family use as well as everyone else- they take abuse easily, are lightweight, very comfortable to stand, lie, sit, and kneel on, and less expensive than hardboards (this one was 6 hundo fyi.
I saw parts of town that I guarantee most folks would never believe are there. Tide was high so I ducked low to get under the rail road and I95, went against the current all the way to Rt 1 (goes from FL to ME) and then with the current all the way back. Saw lots of very large, cool crabs. Nabbed a decent amount of litter but there really wasn't too much out there.