You may want to think about mounting a small trolling motor. It's just easier to fish if you don't have to mess with a paddle all the time, picking it up, putting it down, not having it float away, tangling a tether, etc. You can save the battery by paddling to where you'll start fishing and then secure the paddle and switch to using the trolling motor. Since you are not focusing on kayaking, just get an inexpensive aluminum shaft kayak paddle like you'll find at any canoe/kayak float outfitter.
