Kayaks are the best. The Kaw runs along the JoCo line, and there are public ramps in DeSoto and Cedar Creek in Olathe. You can put in there and kayak to the Edwardsville boat ramp. Cedar Creek to Edwardsville is 19mi, I kayaked that in 89 minutes when the Kaw was running bank full, almost flood stage. It was totally awesome.
Logistics are not too bad, you need to drop a vehicle capable of carrying the kayak at the Edwardsville ramp, and then go to an upstream ramp with your boat and float to Edwardsville. I carry mine on my rooftop rack on my car. I drove 1500 mi each way to the gulf coast so I could kayak in the ocean. Never had any concerns about the kayak blowing off the car.