That's kind'a hard to say, I've considered trying 3' paddles but decided they would be too long. I'm sure that cutting off the top grip would not work. I use the knob to "hook" on my arm just below the elbow. This morning I was starting to repair a pair of 2.5' paddles and was trying to figure out how to turn the knob into more of a hook. Jack once made reference to a similar paddle for sculling.
I'm toying with the idea and build a pair with at least a wider knob. Just resistiing making a paddle
If you do not want to want another "addiction" (paddle making) you could modify a cheap store bought one. Cut the grip off and then attach a new "grip"/end shaped to extend over your arm more. This video shows a couple of paddles made with grips attached to one side . Check out the video at 1:25 min. there is a design that might work for your style.