That is interesting, Marty. And you're right, it does sound quite different.
The first thing that came to my mind was that "Mind your step" is not very commonly said at all, so while it might be kind of cool to have something like that in the sketch, it does seem a bit unnatural to say. Also, I do think saying "Watch your step" sounds a little bit more caring. To me, the word "watch" is a little bit of a stronger word so it would make a bit more of an impact. Like saying "mind your step" seems like something you'd say if the situation were smaller (like, if there was something on the ground you'd want your friend to notice and maybe walk around to avoid, like a puddle or something) while saying "watch your step" sounds a bit more nurturing. ... Even though technically, no matter what word you say, you're saying the same thing, I do think "Watch your step" is the best choice!
But that's just my weird opinion, hehe. I'd be interested in hearing others' opinions as well!