Dealing with Cold, Numb, or Tingly Fingers, or Sore Wrist or Forearm

Shift your grip hand - rather than holding the top of the paddle rotate your hand so your palm is across the grip (using a Northwoods or Palmed grip). The paddle grip on the right is elongated grip to make use of the palm easier but this shift can be done with any pear grip as well.

Different blade - if you have the opportunity change to a narrower blade, such as an otter tail. You may not feel as much power but these paddles are more forgiving with regard to repetitive strain injuries. Otter tail blades also tend to be a little more flexible, try a paddle with a little more flex in the blade and shaft.

Alternative grip - asymmetric grips ('ergonomic') can be helpful for straight paddling. Although T-grips provide much better grip under tough conditions pear-shaped grip are less likely to cause repetitive strain.

Shaft shape and size - many people find an oval shaft provides relief from strain. 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.  Unfortunately, paddle diameters are not usually provided and the size is often discovered by trial and error.  

Bent Shaft 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 a 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.
Paddle Length - 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.