When paddling you might experience cold hands, numb or tingly sensation in your fingers, or sore wrist or forearm. These sensations are often connected to irritation or inflammation of tendons and associated pressure on nerves. Not dealing with these issues can lead to long term injury.
I have several suggestions that may help (in order - easy/free to difficult/expensive).
The following clip I have exaggerated opening my hands or wiggling my fingers. The J or Canadian portion of the stroke is controlled with the palm of the grip hand, the shaft hand provides power, stability, and recovery. The shaft or wrist hand is not rolled as part of the J or Canadian stroke, allow the paddle to move/rotate in your hand.
I find that a paddle shaft with a diameter where my middle finger just meets the base of the thumb (thenar eminence) or the index finger meets the joint of my thumb, to be the best size. I can comfortably paddle with a slightly larger shaft but any smaller I start to get prickly fingers. In any case the shaft should slide through your hand easily.
I should mention bent shaft and double bent paddles. A single bent shaft paddle will not likely change the stress associated with holding the grip or the shaft. Bent shaft paddles more often have an ergonomic grip, and they are more likely to be oval in cross section. Double bent shaft paddles have two (or more) bends, the second bend provides a better angle for gripping the shaft which reduces tendon stress (I am not sure this is true with canoe paddles but this kind of bend is commonly found in kayak shaft 'cranks' for this reason).
There are a few custom paddles that also adjust the angle of the grip (compared to the blade) to provide better wrist angle. Another modification includes using an asymmetric blade. Unfortunately I have never seen paddles with either of these features in use. These adjustments make the paddles only usable on a single side.
While on the subject of shafts - the overall length of the paddle can also be an important factor in efficient paddling and has implications for overall ergonomics. Paddle length overall is another subject (see paddle length write-up).
If you experience associated weakness or chalky looking skin (white) this might be associated with Raynaud's syndrome. If the numb/tingly feeling becomes more chronic you may have symptoms of chronic tendinitis (e.g carpal tunnel syndrome). You should seek medical advice and occupational or physiotherapy.
A related article by Bob Foote may also be of interest: Tips and Techniques - Loosen Your Grip. In addition to the discussion above he mentions alternative grip for T handles, and locating your shaft hand for less stress on the wrist.