Offsetting your balance is only going to worsen and agitate the pre-existing issue. As Az said, don't try to "push through" anything. If an exercise hurts, try some isolation stuff that doesn't hurt to strengthen the area.
Dips hurt my shoulders if I lean forward while doing them (to try and hit the pecs a little). I'm limited to keeping it
straight up and down to minimize the rotation angle on my left shoulder. Again, if an exercise hurts, you can also try the DB alternative.