You will need heavier wheels than that for a cannon. Back when I was doing re-enactments, we went through a lot of lumber before we got it right. Even when we were only firing blanks it was hard on the carriage and wheels. Wound up making everything out of white oak rescued from an old barn. Wish I had some pics of that old gun. A buddy of mine who moved out of state has one taken at dusk that is awesome, wheels off the ground huge muzzle flash and it looks like a shotgun blast coming out of the touch hole! Best of luck in your cannon build!
Whitmer Coach Shop in New Holland PA makes cannon wheels and they sell all types of parts for horse drawn vehicles. They have a catalog and do mail order but it is worth a trip to see what they do. It is an Amish business so no Sunday Sales, no web site, etc. They have made carriage wheels for me. And I have seen a cannon sitting outside their shop with its new wheels.