It's surprisingly often that I meet or hear from people who don't know that you can L-cancel by tapping the shoulder button. Pushing it in all the way is not necessary at all, and tapping it doesn't ruin your tech timing, nor does it cause you to air-dodge, because you never clicked the shoulder.
I definitely don't think Z is superior. In fact, it requires more pressure to press Z than it does to tap a shoulder button.
Either way, do what works best for you, but definitely try them all so that you know for yourself.
EDIT:
And to answer the question of this thread: Yes, it's completely possible to beat someone with superior tech skill. What matters is how intelligently you play. Dash dancing is a good substitute for wavedashing if you're not good at it. L-cancelling should be attempted every possible opportunity. Even if you're not good at it, force yourself to try it every time. It will quickly become second nature. (The last two statements of this paragraph apply to everything, really)
I highly advise you pick a character, go to Vs. Mode against a Level 1 or Human (just standing there, so you can practice without interference) and familiarize yourself with the speed, range, duration and other properties of all the moves you have available. **In case you're not familiar, I advise Vs. Mode (Melee Mode) instead of training because training mode does not allow you to use the C-stick for aerials, Smash attacks, rolling etc.