I make mine walk because most of the time the kids who have to miss recess are the ones who need to get some energy out.
How is walking any different from what they will be doing a few minutes after their laps are over? I wouldn't use running because of asthma and just because it is more a liability, but these kids walk in the hallway, to lunch, to art, to the bathroom. Walking laps around the playground is not different.
But if your principal doesn't support it try something else. I like to have them write me a paragraph about their offense and then the steps that they would take to correct it. They ususally hate that.