With appropriate gear reduction it might work. Depends on what you want to use the wood chips for. If they need to flow, as in a self feeding hopper I expect the "chips" would be more like splinters and bridge (ie wouldn't flow). If simply for disposal and mulch would be a good way to get your exercise.
I would imagine if you could have a heavy fly wheel it would work for light shredding of mulch etc plus it could be operated single handed. Get it up to speed by going up through the gears then jump off the bike and throw some stuff through. If it starts to slow down you jump back on the bike and get it back up to speed.
I've seen a small, bicycle powered chipper/shredder built for household and greenhouse waste. They took the geared wheel off, wove wire between the spokes, then filled the space between hub and rim with concrete. This made it a flywheel to give the grinder more consistant power. I don't remember if they made it where they could change the shredder out with other things, pumps, etc., or made other flywheel bikes for other uses.
There are too many new and different mistakes out there waiting to be made to be wasteing your time repeating the same old mistakes.
what about smashing it first with a pneumatic or mechanical press, THEN blending it? also if you put a large metal disk as the one that is powered as you petal you will get to use the forward momentum of the flywheel to blend or chop your cane?
I use my strimmer with a 3 tyne metal blade attached to shred up all my leaf and twig ... it will chop everything including branches up to 1" dia to a fine mulch. Easier to do it in a big barrel, like a food processor, or wait till you have a pile then just strim it down, against a wall is best so it doesn't fly all over the place.
I think you could probably weld an axle, hub, and cassette assembly right onto the input shaft of the machine and put your mountain bike right on there. The spinning blades of the shredder should provide enough inertia to act as a flywheel once you get the thing up to operating rpms. I think an electric motor, solar panel, and a bunch of car batteries would help too, or else you may have to feed it so slowly that it wouldn't be practical, depending on how strong or how patient you are.
You know it is dark times when the trees riot. I think this tiny ad is their leader:
Whom would you place at Level 9 on the Wheaton Eco Scale?