I've been trying this for original Umihara. I'm not quite done yet but wanted to report how I've done so far. This is without collecting backpacks, by the way. Field 50, in particular, I can't imagine clearing without jumping after getting the backpack.
Fields where I've had to jump to clear:
Field 2, both exits (one jump - at the start)
Field 11 -> 12 (one jump - can get to the floating platform to the right of the F12 exit without jumping, then jump over)
Field 17 -> 30 (one jump - over the spikes next to the exit)
Field 33 (three jumps - over the gaps between ice platforms on the upper two levels)
Field 42 -> 43 (one jump - slightly uneven ice platforms at the end)
I'll update once I've done fields 40 and 49. Update: It wasn't exactly pretty, but F49 is done. Update 2: F40 is done.
Update 3: I've cleared Field 50 with no jumps after collecting the backpack.
Update 4, Nov 22: I've cleared Field 2 without jumping at the start. Thanks again to PewableShift for showing me how!
Update 5, Dec 19: I've reduced the jumps for F11->12 to one.