I like the mini-paddle idea, basically an over-sized ping-pong paddle, heard they have been given out at boat shows in the past...
I use the T-handle end on half of my Hobie paddle and keep that 3' paddle stored in a manner that lets me grab it quickly with one hand. If I need to use both hands to maneuver then I drop the rod into one of the rod holders...
I only carry the full length double ended paddle when I am going into the ocean.