We have quite a few customers who ask about solar charging on a kayak. We spoke to the folks at Voltaic Systems who came up with the solution for solar charging laptops, ipads and phones whilst paddling.
See the following link which relates to the Voltaic Solar Laptop Charging package: http://voltaicsystems.com/blog/gear-winner-update-indonesian-seaweed-research/
One option is to put the battery in a dry case - in the US they call them Otter Boxes or Pelican Cases and connect to the battery inside the case. You would need to drill a hole in the case and seal it with something like silicone to make it waterproof. Or a storm-proof, but not waterproof solution would be to put the battery in a dry bag with a roll-top.
Another solution is to put a solar charging system such a Voltaic or Goal Zero solar panel and battery in a clear faced dry sack and attach it to the kayak.
If you are around salt water, you should cover any connections exposed to salt water with silicone tubing (looks like this : http://www.freshwatersystems.com/p-9001-silcon-silicone-tubing-18-id-x-14-od-x-1.aspx?utm_source=Googlebase&utm_medium=Feed&utm_campaign=Product&utm_term=280-0204&gclid=CM-JjYeSibcCFc0r6wodt2QACA). It's also advisable to rinse any salt water off with fresh water if it accumulates on a connection.