I was wondering if there is a way to use audio-snap and have the full wave move instead of it stretching or compressing the note in X1 Producer.

I haven't used AudioSnap in a long time because it almost never worked correctly for me.

With that being said, I think I remember the manual explaining that when using AudioSnap with drums, moving and crossfading regions was recommended because stretching and compressing drums can sound weird. There's probably a mode in AudioSnap that allows you to snap with no time stretching or compression.

How many sections do you want to fix? If it's just a few sloppy notes, you're better off cutting up the parts and moving them around manually. If it's a lot of fixes and AudioSnap isn't working for you, there's other ways to get the job done.

You  can use split at beats and then move the clips that are created rather than stretch the audio. Especially useful on drums and works quite well with quantize.

Remember to control clip size use the threshold and resolution controls to filter the transients.