I am not an expert on the laws regarding infrastructure in old Japan, but it was my understanding that the rules against using wheeled carts and such was only concerned with the major roads, mainly because the over-use of carts would wreck the dirt (and because of rain, often muddy) main thoroughfares. This is the reason palanquins were the main means of transport and why seige weapons saw minimal use.

I don't believe, however, that wheels themselves were outlawed. It would seem odd to deny a farmer the use of his ox cart around his farm, for example. Granted, I don't know how historical a small cart like Lone Wolf & Cub's would be, even before you consider all the weapons he has hidden on it.