Question: Are we talking about the jump button, or actually jumping? Because THZ2 (and I'd wager plenty of other stages) is possible without jumping, but you need the jump button to trigger the whirlwind shield when walking off ledges. Actually, it's almost trivial once you get the shield.
I haven't done much in this category but here are some preliminary thoughts:
THZ1: Need a jump right at the beginning to get on the pipe.
THZ2: This pipe you can just walk on, however. Once you get to the drop off before the whirlwind shield, you can charge a spindash to get to the pipe on the far side of the room. From there it's easy to get the whirlwind shield. Without the shield, you can walk off the pipe onto the spring shell to get across the room, spindash into the next room with the moving blocks, and here I believe you'd be stuck. It may be possible to damage boost using the buzz from the previous room but I haven't tried it.
THZ3: There's no high ground to get spindashes off.
DSZ1: I think you'd be stuck at the room with all the skims right before the collapsing platform and attraction shield.
DSZ2: How to get out of the pool:
https://gfycat.com/VacantTornAfricanclawedfrog This map is probably stuck when you have to jump over some spikes in the underwater slide though.
DSZ3: Haven't tried it but it should be possible to spin into him. You'd have to be really quick getting onto the capsule before it rises though.