You wouldn't be able to cut a single layer and ripple delete unless you have a gap that could be rippled. Unless I'm missing something that means you would have to cut all the other layers in order to ripple delete.

Edit: I didn't realize you were asking to ripple certain tracks. This can be useful, but also dangerous if you accidentally ripple with some tracks are locked and you're zoomed in so you can't see that you just broke the sync on multiple clips.

You can, however, use the Lift command (shortcut is the semicolon key) to delete an In/Out range of just targeted tracks. I have my track targeting mapped to the keyboard shortcuts 1-9 for V1-V9 and Opt+1 - Opt-9 for A1-A9. This allows me to very quickly untarget all of my tracks except the one(s) I want to remove footage from, hit "X" to mark an In/Out range over a clip on the targeted tract (no need to even select the clip, just have the playhead over it) and hit the semicolon key to Lift that clip out.

The Extract command (shortcut is the apostrophe key) will ripple delete an entire In/Out range regardless of what tracks are targeted.