Great ideas! You have a few options. Now you can scratch a bigger hole in your head Lol!!!!!
Do you want to shorten your paddle? Then now is a great excuse to do it.
If not, find where it is leaking first. As said, Put paddle in sun. Check any bubbles, water leaks at the joints. Usually it is the handle. Glue does perish after a while. I have just poured boiling water over the joint area & the handle just twists off.
If handle wont come off & it is leaking at the joint. Just drain as best as you can. Drill holes if you have to but a little water wont hurt & as long as the paddle floats easily then good. Then sand & clean around the joint. Apply tape around the shaft on both sides of the joint leaving about 3mm gap on both sides of the joint. Then apply epoxy over the joint as you turn the shaft continuously so it doesnt drip! Then before it hardens, peel the tape off & continue turning the shaft until epoxy hardens. This should leave the joint neatly covered with 6mm width of epoxy to ensure a waterproof seal.
Hows that for a short answer. Lol!!!!!