Creating a kayak paddle power meter

What about a bending beam load cell?

I bet the commercial products use strain gauges (the OP's original thought). If this were my project, I'd start with those. It would be very simple (relatively speaking) to epoxy four of them to the outside of the shaft, spaced at 90 degrees...

Ok thanks for the advices!
So 4 strains gauges in a Wheatstone bridge? Is that the application?
Thanks again, I figure out little by little!

No, bridges, plural; i.e., more than one, to capture the biaxial bending and, possibly, torsion, if significant. And for best results, there would be at least two individual strain gauges at each of the four locations.

Frankly, based on your posts to-date (nothing else to go on, of course), my impression is that you currently lack the science and engineering skills necessary to pull this off. Not saying you can't do it, but I think it would take an enormous amount of self-education. And even then, success may be difficult to achieve.

So, you would be doing your Olympians-to-be a huge favor if you directed your DIY energy into fundraising to buy one or more of the commercial products. They're not that expensive.

Or, if you really want to reinvent this rather sophisticated product, attempt to engage the ME, EE, and product design faculty and students of a university near you.

I agree with DaveEvans. If you really want to do this yourself, plan on a couple of years of research and development before a functional and actually useful product could be expected.

For sure you’re right! As a lot of people at the beginning of the learning curve I was far from understanding the difficulty of that project.
For sure I can invest in buying directly the shaft with the power meter installed, which is not so expensive compared to the investment in time needed by myself to get something usable.
I saw it as a mean of personal skill development, but it looks like I miss too many basics in electronics and engineering.
I thank you again for your help and the time spent on answering me.
I’ll still try to make it work, I’ll let you know if I come close to a solution, which I doubt now.
Thanks again, best regards