Others will probably chime-in, but here's my $.02:
There has been discussion here in the past regarding varnish/no varnish on cane. My own life-experience has involved replacing seats and other caned areas in antique furniture for an antique shop, and in the case of antiques, the cane isn't varnished unless it had to be stained to match old cane on the chair's back, which wasn't damaged, etc.
Cane has a surface that naturally appears to be coated with varnish or shellac. Sometimes, this wears off. Then, a coat of varnish or shellac could make it look okay again.
In your situation, washing with soapy water might help. If the reason the cane appears dirty is that the natural surface of the cane has worn off and dirt is imbedded in the cane itself, bleaching may help. In that case, I'd try oxalic acid-- which comes as a powder and is dissolved in water. Wear gloves when using, but oxalic acid doesn't dissolve skin-- it's what makes the surface of your teeth feel funny when you eat spinach.
Don't be afraid to experiment, because re-caning canoe seats may be the easiest part of the restoration process of a canoe... so, if the seats don't look good to you after you've washed and bleached, they can be re-caned. Trust me, even I can do this. I've known blind people who cane seats.
But maybe the seats have an interesting patina and if sturdy, are okay as-is. It never hurts to post pictures and get a group consensus
![Smile :) :)](https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f642.png)
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Kathy