You may want to try a "hydration belt" - you know, the ones with the little 8oz bottles. I'm not crazy about them, but they do work. At a minimum it saves having to hold and carry a container in your hands for whatever distance you are doing. The biggest complaint about the hydration belts is the jiggling, but I find that after about a half mile things settle down into a comfortable spot and I don't even notice the belt. Also, having more than one bottle gives you the option of putting water in one and a sports drink in the other... just a thought... good luck with your neck!
-bill