First, do as much of the carving as you can. Then, check the moisture content [I suspect that the wood is dryer than you think.] If it is fairly dry, then toss it in the crick for a while [a couple of weeks] and see how much it swells up.
As the tree has been dead for a while with no sign of rot, I suspect the sap [which is what rot fungi love the most] is mostly out of the lignin. This means that what is left should be fairly light until you resaturate with water.
If the check is fairly small, under 1/4 inch, carefully install a stop [driven dowel coated with epoxy] about 6 inches past each end of the check. Your next step will depend upon how long the check is. If it is under a foot or so, let the boat dry for a week or so to allow the seam to expand slightly, clean it of loose fibers, caulk it with cotton and roofing cement an go boating. If it is much bigger than that, you will have to install "floors," supporting ribs which maintain the relationship between both sides of the structure. You can then fill the check with a putty of epoxy and wood powder. [You can use sanding dust for this application but the finer the dust, the better.]
Once you have made the hull solid, you can decide whether you need a ballast keel for the boat. Small sailboats, including canoes, do not need a ballast keel. I teach sailing in canoes and all we use is a leeboard. Never had a student get dunked yet. ah hu, ah hu.
If you find that the check does not go all the way through, you can fill it with a mixture of sawdust and beeswax unless you are in a part of the country where the beeswax will liquefy.