I've dealt with rotator issues in my right shoulder for a couple years after hurting it doing decline bench.. and my left shoulder is jacked up from a motorcycle accident.
I still have a decent capped shoulders
I've been able to continue to develop them through injury though,, through doing time under tension and isometric holds.. very very light weight that is pain free, the delts themselves don't need a ton of mechanical tension to grow. just the frequent constant tension will keep them stimulated and growing. you don't need to press.
if dumbbell side laterals hurt. try using a cable and only use one plate of the stack. super light and pain free. but make each rep last a good 40 seconds. contract the side delt and make that contraction slowly move your arm up, taking about 20 seconds to get to the top. then squeeze and hold it at the top, then slowly slowly let the weight back down . your delts will be on fire, yet it will likely be pain free in the joint.
there are other techniques as well . I may start a thread on ways to train around injuries and still get good muscle stimulation.