The canal authority does not require 3 crew. In fact, they have no requirement at all as to number of crew, except I think they prefer a crew number > 0.
Transiting the canal *could* be done singlehanded on a boat your size, but would require you to be an expert in handling your boat. It might be good to transit the canal in the off season (September rather than August) to avoid crowded locks. Less boats means an easier time if you do flop around a bit in the lock.
I think a good way to lock through single
handed would be to align your boat up amidships with the line that runs vertically up/down the lock wall.
Grab this line (bring gloves!) and steady your boat, or possibly pass a line that is cleated to your boat amidships (and loose on the other end) around this line at your midship point and steady the boat as you go up/down the face of the wall.
Put out generous fenders on the bow and stern in case you end up twisting due to currents and having either side bounce off the wall (touch the wall, really - it won't hit hard).
We used fenders with a 2 person crew (one crew only 100lbs) for the first lock only. We found that fenders weren't required if you handled the boat well. You can push the boat off the wall pretty easily - even our 26,000lbs boat and even with a fair amount of wind
To make a long post short, I think as long as you can find a single
point from which to control your boat's alignment with a dock
- practice first at home), you can use the same technique when locking through. The principle is the same.