I haven't been kayaking at HH. However, I do go kayaking every once and a while. In general, I find kayaks to be much more stable than canoes. This is partly due to the fact that you sit much lower and this reduces the center of gravity.
It is possible for kayaks to tip over. However, I've never had it happen to me, but I mainly kayak in relatively calm water. So, I think it all depends upon the conditions where you are kayaking.
Also, depending upon the kayak and the conditions it is possible to get wet. It's not unusual to get a little water in the kayak from your feet when getting in if you're launching from the beach. Also, water can splash in from waves and some can come from the paddle.
My family really enjoys kayaking and we're hoping to go to HH next year and definitely plan on doing it.
If the weather is reasonable, I'd say give it a try. It can be very relaxing and doesn't have to be strenuous at all unless you go somewhere that you have to fight the currents.