Suggestions, please..
 

I have access to just a regular, non-fishing kayak andI want to take it out on a pond down the street. I just fit in the thing as I'm 6'3" and I'm wondering if there is any practical way to secure the paddle while fishing? I was thinking about a bungee, but I'm still thinking it will be a PIA to switch from paddle to rod. Thanks for any input...

No such thing as a "non-fishing kayak"! The paddle kayak fishermen have to paddle and work a rod at the same time....its just the nature of the beast and they do quite well at it! Us Hobie folks....not an issue but you will get used to it...give it a shot!!

They sell a lanyard for the paddle. You might be able to find a cheap one at #^&#^&#^&#^&s.
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Paddle Leash...they have them on Austin Kayak...

Bungee Paddle Leash - Austin Kayak - Product Details

Thanks guys

Get a paddle that floats. If it falls in the water, just reach in and grab it.

Floats....with a leash. no leash and it can still float away....just as bad as sinking. Either way you're sitting in a kayak without a paddle.

Better than if it sinks!

True....