For wavedashing out of shield I don't imagine anyone would use a different input method to jump than the one they use for normal wavedashing; I can't see any comfort or practical reason why one would do so. The same would apply for jump cancel grabs.
Spacie players are more likely to use the Y button (at least for some inputs) because it's closer the the B button (which needs to be used for shines/lasers immediately after or before a jump), though many spacie players still use X to jump regardless due to preference or habit (including Mew2King, and Dark as previously mentioned by Victra). Personally, for shine out of shield I claw the Y button with my index finger and press the B button with my thumb (I normally jump with the X button).
Don't worry about which input method is optimal; the optimal method is necessarily whichever one you can preform best (so long as the end result is the same). Just try different methods until you find which method that is.
In Brawl and Project M you don't have to press the control stick as far for the game to register it as a dash as you do in Melee, making it easier to dash (and correspondingly harder to walk). Dashing in Melee is not actually difficult if you have a good controller though.
Brawl has an input buffer which is not present in Melee or Project M; this makes the timings on many inputs much more lenient (including dashing immediately after the lag from something else, since you asked about that specifically).
Advanced techniques in general aren't easier in Project M, though some specific ones are for various reasons that I lack the knowledge to discuss.