Looking through the dumped images of the levels from the Neo Orig and Extra Lemmix players, these levels should be possible (but untested):
Orig 2P levels: 1, 3, 4, 5, 6, 9, 10, 12, 14 (due to the exits being next to each other), 18 (same reason as 14), 19 (same reason as 18 and 14)
Extra:
Genesis: 1, 7, 10, 11, 13, 16, 18, 20, 24, 25, 27, 28, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 41, 45, 47
Present: 6, 7 (but the 99 release rate makes this one very difficult), 9, 11, 12, 16, 21, 22, 26, 27, 29, 30
Sunsoft: 7, 8, 9, 11, 12, 15, 19, 22, 23, 24, 26, 27, 29, 30
Gen 2P: 2
Sega: 1, 3 (possibly, but it can be very hard to squeeze through the gaps), 7, 10
PSP: 1, 2, 4, 7, 8, 9, 15, 16, 17, 18, 20, 22, 23, 24 (possibly, requires a trick on the very left side), 27, 28, 29, 30, 31, 32, 33, 34, 35, 16
Other: 1, 3, 4, 5, 7, 8, 10.
One Way to Freedom will be added to the Neo Extra player in a future release; this one should also be beatable. The position number of the levels in Other will be changed to reflect this.