So, to be serious, your whole body is meant to work together, and it's best not to spot train specific areas. Muscle imbalances can create all sorts of issues.
If you really only want to do the minimum, core exercises that use your whole body are great:
Exercises that use all the muscle groups are ideal (I'm talking weight training here):
forearms and hands
Then, especially for kayakers, the all important shoulders need to be hit in all areas:
Cardio is important for your heart and more importantly, your brain. Yoga or some sort of stretching rounds it out!