Try one of these...
http://www.petco.com/product/9799/Ga...tackables.aspx
Lay the back down to where the lid is on top. Seen a lot of guys use these for their kayaks. They mount rod holders on the back or sides and they're set. Mostly seen it used with water pump to pump fresh water in and old water out like they do on a baot. Not sure if you want one for a kayak, just thought i'd throw that in.
The ice is a good idea to keep the water cool, so is a round container for shrimp. What I do is weigh down a sponge to the bottom. Gives the shrimp something to grab a hold to so they are not banged around as much.