As a lifelong swimmer, and current SUP and outrigger paddler I can give your first hand knowledge of both sports. Swimming can target back muscles, but most directly if you swim predominantly backstroke. For freestyle, breaststroke, and butterfly, the back muscles are primarily used in recovery motions and are very lightly loaded. In backstroke, if you are using good technique, you will be targeting mostly your latissimus muscles and to a lesser extent the muscles of the upper back and shoulder.
SUP paddling differs from swimming in that the stroke puts a much greater load on the entire core because the force of the water on the paddle has to be transmitted through the entire body to the feet, which are the only things that move the board forward. The stroke itself will also directly target the latissimus group along with almost every other core muscle group from the upper chest, abs, obliques, psoas, through the pelvic girdle, to the legs and to the feet.
As you might gather, SUP paddling (done correctly!) is a very complete total body workout, including your legs, although in a different way than running. Your legs will not sustain any impacts with either sport, although backstroke will target your quads through kicking much more than you might expect.
If I were to recommend a cross training sport for anyone, SUP paddling would be at the top of the list. If you are using good technique, you will feel it from head to toe. You will also improve your balance, coordination, and aerobic capacity. I would definitely recommend it but with the caveat that you do it correctly - including getting a lesson or two - to prevent injury and to get the most from the sport.
As to your original question about targeting the back, SUP would be the clear favorite for cross training, but your legs won't be resting. They will be engaged as stabilizing/transmission muscles so they will be used in a very different way than running.