Is it a good idea to bring a dog with you in a canoe, kayak, SUP board? It doesn’t really matter to most people who want to do it — they are going to try it. I suggest they make their attempts safer and more positive and hire a dog trainer to help.
Getting reputable professional help from a dog trainer who specializes in compulsion-free training is essential. If you rely on leash corrections in your training, it is unlikely you will be able to while you’re managing a paddle and trying to remain on top of the water? If your dog has a poor recall, what is your plan if your dog jumps in the water and starts swimming away? Yelling at the dog to come back to you isn’t likely to motivate your dog to come to you (or reduce the likelihood that your dog will not jump into the water again in the future). It doesn’t work to improve a recall on land, so it is unlikely to work in the water. If your plan is paddle after the dog furiously and then scold the dog for jumping in or for not coming when called, that’s isn’t going to improve your dog’s behaviours, either (on land or in the water). Both of these options in effect reduce the likelihood that in the future your dog will stay in the boat or come back to you. It’s science, not an opinion.
Does your plan involve a leash to keep the dog with you? It can be unsafe to have the dog on a leash while in the water: the leash can get caught on things under the water, not to mention the leash can get caught on you and possibly injuring or dragging you into the water as well.
Please don’t even think of using a shock collar in a water environment. Or a bark collar. Or any electronic collar. I’m sure there are trainers out there who would recommend them, but use common sense, please.
Why not train your dog for this? Find a trainer to help you teach your dog to enjoy the water and to show good manners and impulse control while around water while at the same time building a bond and making the experience pleasant for both of you. A little time and effort into training before heading onto the water will mean a lifetime of water fun adventures for you and your dog.