I know the answer is probably no, but sense it is possible to beat the game jump-less could we get that as a category. Also I am willing to do a full run as proof if needed. Overall this would probably be a funny run if it was implemented.
1-2 is possible jumpless in singleplayer but very hard:
I am aware of the jumps from the shell, but idk whether or not it should count as a jump. Even if 1-2 is possible jumpless, 2-4 is impossible after you enter the 1st pipe. But I think a minimum jump category would be challenging but fun as it would probably be harder than even MINIMUM CAPTURES in SMO!
After thinking over it, I don't think that that koopa shell should count as a jump. So 1-2 is possible jumpless that's cool.
https://www.youtube.com/playlist?list=PLJ4AKD0G9IScCsd4omgqCNJtvRCp80YFO
a playlist of my single player jumpless vids, i'm at bowser-train with 23 jumps, close to beating the game