I have taken my guitar on float trips, with the instrument wrapped in a plastic trash bag and then set inside its case. I haven't had any problem with normal splash. If the canoe were to actually dump over, water would probably seep into the case and perhaps the trash bag. A fiddle, being smaller, would be easier to get a secure wrap on using plastic bags.

Canoe bags, as mentioned above, come in various sizes and various quality levels. The better ones would likely survive submersion for a fair time. The cheapies may not be much more water-resistant than a trash bag, but they are more durable. A homemade bag can be fashioned using a fairly thick plastic trash bag as the inner liner and a durable (puncture resistant) canvas or similar outer bag. A watertight (or at least highly water-resistant) closure for the inner bag can be made by rolling the top of the bag several turns on a round dowel stick and clamping it in several places with binder clips, those triangular-box style paper clips.

If you're going to be in the Missouri/Arkansas Ozarks area, I might be able to shed some light on the "dumping" potential of the river you'll be on.