Just cut down a trolling motor and rig it off the stern or side. I had a 12V Walmart by Brunswick 40 lb thrust motor I found in a telephone closet of an abandoned building. I was going to gut it and use it as a bike tire traction motor but ended up selling it for 40 bucks. They were cheap ones on craigslist. That would get that kayak going on the long trip back or into a headwind. Invisible depending on what type of battery you were using. I used 2 smaller '5 lb' 7.2AH 12V gell cells from a battery back up in parallel.
