Get a chance to watch Rip's fairly recent vid on it? How to do Dips | Mark Rippetoe.
Bill Starr has some good advice (IMO) also regarding easing into them before adding weight, and doing them safely: The Quest for a Stronger Overhead Press | Bill Starr.
Rip says in his video to avoid or be very careful w/ Dips if you have rotator cuff problems. That said, I've had (non-training caused) injuries on both shoulders, probably one of the rotator cuff muscles for each of them. When either Bench and/or Press started to bother one or the other, I'd drop Dips into the program as a replacement - typically for Bench. Usually, for whatever reason, the pain would resolve while still allowing some gainZzz. I've never had a diagnosis, so my injuries might not even be relevant to yours though.
Also from what I've seen, Andy Baker almost always prescribes them as an assistance exercise at lower intensity for higher reps - sounds like that's what you have in mind.
I've never felt any impingement doing them more or less as described in the book and the above video, going just to or maybe slightly below "parallel".
Good luck.