This is what I use to bring collapsible hiking poles from the US to the UK. My $35 duffel bag has a bottom compartment, where I put the poles, wrapped in bubble wrap, along with my hiking boots. It may be harder to accommodate the greater length of the kayak paddle.

I believe the extra baggage charge is $100 for one extra piece, not $235; $235 is for the third checked bag. However, it looks like your paddle bag dimensions would exceed the maximum 62" combined dimension requirement, which could cost $200. You might get away with it since it is so light and would not exceed the combined length-width-depth by very much.