If this paddle will actually be used, rather than be a pretty wall-hanger, or "prop", you need quality wood. The wrong wood or cut can warp, can be too flexible and can be too heavy.
Most people look for western red cedar or spruce, with vertical grain (if you place the board on its face and look at the end of the board, the grain will look like |||||||. Ideally the grain, that will look like pinstripes, will run from one end of the board to the other. If the grain runs diagonally and exits near the loom, that can lead to a break. Very small knots in non-critical places can be OK.
You CAN find good cedar at your local box store, but you will probably have to visit a large number of them. I have had most luck looking at the 4 X 4 cedar posts. Assuming you find a clear one with good grain, and have the means to shape the stock, that might be your best bet. If you have a quality lumberyard, visit them and ask to look at the clear, vertical grain western red cedar.
You can find information on making a GP on the Qajaq USA website at http://www.qajaqusa.org/Equipment/paddles.html .
4-place Boat Trailer
1 Canoe/Kayak Trailer
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