Not sure if CT would agree, but if I understand correctly what you’re intending or hoping to do, I don’t think it would make a difference (except maybe to make it either more or less uncomfortable on your WRISTS).
- Pressing is an open-chained motion: limbs move an external weight around or away from the body;
- Dips are closed-chain: weight is the body itself, which the limbs move in space around a stationary object.
So even though you’re using the same limbs and main muscles in both exercises, the effect on the shoulder joint is somewhat different. Angling the stationary “thing” you “press” in Dips (bars or handles or whatever) wouldn’t have the same effect on your shoulder as happens when you tilt the bench on which you lie to press a barbell or dumbbell. In the Dips example you’re of course not really pressing the dip handles, but pressing AGAINST them so your body rises away from them, against the pull of gravity - the body goes pretty much straight up. In Bench Press variations your shoulder moves weights through a slightly different arc or range depending on where your torso rests, which in turn obviously depends on the angle of the bench. Gravity always pulls straight down; therefore changing the angle of the bench changes the extent to which the shoulder joint is exposed to the load at various points along it arc or ROM.
In Dips the best you could probably do for such a source of variation is try to push / rise in more of an arc, or lean your torso forward while pushing (think sort of like mid-air Push-ups, or the opposite of Lean-Away Pull-ups). BUT I have tried this before, and believe me, if you have shoulder troubles you will probably NOT find that more comfortable.