Besides gondolas, are there tours of Venice's smaller canals?

Even if you found a guide with a boat, you would still be paying water taxi prices, probably more.
You might start by checking Viator Venice.

Thank you. I had forgotten about Viator. Are they reliable?

Viator simply markets other companies' tours. Therefore, the quality of the tour is under the control of the tour operator, not Viator.

I use context travel throughout Europe, and I've only had good experiences. In Venice, I took a an overview of Venice that was done in a water taxi, with six of us on the tour. I don't remember the name, but you should be able to recognize it on their website, or phone them at their US office – the customer service is quite good. As I recall, the time was largely spent in small canals. I remember we finally got to very small side canals where we couldn't go under a bridge because it was high tide and the bridge was low.

Thank you for the great tip!

When I was in Venice last month I saw several tour groups using kayaks on the small canals. Looked very interesting. I'm sure if you google "Venice kayak tours" something will pop-up. Although may be a little chilly in November - perfect opportunity for warming up with a cafe corretto after your tour..

While there for a week I hired a water taxi by the hour and avoided the packed streets full of umbrella leaders of tours. In two hours I was able to relax in small canals, stop and get out for a snack and then go to Murano for glass factory appointment, to Burano to photograph the beautiful colored villas and return to watch sunset on Grand Canal. I walked around the water taxi area close to Rialto bridge and negotiated the rate.

Next evening I used the same driver for an evening tour. You can look into the windows of some of the grandest villas and see the amazing frescoes and chandeliers. The waters are calm and you can bring along a picnic with Prosecco. I paid €80 an hour. It would have covered up to 8 people. Sadly I didn't know anyone else to invite so it was me and Jake. Do not hire gondola or water taxi at St. Marks. Way more expensive and too many tourists. I found a gondola on a side canal behind St. Marks. Very nice craft and gondolier sang and had fun too.

I saw the kayaks but honestly the traffic of gondolas and water taxi in small canals during the day was making it tough for kayak to navigate. Water is cold too.

Consider doing something unique and support a Venetian tradition at the same time: rowvenice.org

Tell your instuctor you want to stay in the canals the whole time and not go out into the basin.