Let's not forget the benefits of DB Upright rows. Which are suggested to be done one arm at a time, rather than together. With a free hand I will grasp a support, as a post, machine, etc. DB's allow a more natural feel to the wrist, elbows and shoulder joints themselves, when doing this exercise (and most every other exercise in my view). Keeping the grip and pulling position too ridged may produce unneeded stress on the wrist/elbows/shoulder joints throughout the complete pull, as a BB will tend to do. Allow the DB to come up a little wider and out when doing it.
If undo stress is felt when doing Upright's than switching to the DB version (or cables as the lovely Princess L suggest) might relieve this factor. BB Upright rows can be mistreated by a lot of people when the bar is lifted too far out and away from the body. Keep the bar close (almost touching) the body. Raising the bar too high may also cause stress. Between the upper to middle pec should do just fine, not the chin. Too wide a grip can cause harm. Pick the grip that suits you, not what is usually advised in training articles. Most important, warm-up before attempting this (or any other exercise). Might try using a empty light exercise bar and doing at least 20 full reps for a couple of light sets.
I am bias about Upright rows (BB & DB) because it has been one of my favorite exercise throughout the years. Never had any problems, which also goes for other men I have known, who have trained heavy and with serious intent on it. Can always depends on it to add muscle mass and strength to the whole shoulder girdle. Just hate to see it misused by a lot of trainee's. As far a rotor cuff damage is concerned, for observation I would believe that more cuff tears have resulted from doing bench press than any other upper body exercise I can think of. Including the fore mentioned Uprights and the press behind the neck. Good Luck.