It will be a slow process (service records take many months to obtain), but once you have a death certificate in hand, I would certainly try to get his service record from Library and Archives Canada with the information that you have so far. See the link below for more details. As he has been deceased for more than 20 years, his file will be available (that is a major hurdle to overcome), and my experience with the Archives is that they do a good job in working to figure out which file is his, even when working with limited information.
More details on where he was born, where he enlisted, his parents names, etc. are all helpful, but not strictly necessary to find his file. In the worst case, they say they can't find him without additional information and you carry on with your research to track those down. In the best case, his file will answer all of those questions.
http://www.collectionscanada.ca/gene...909.007-e.html