what is the type of cellular respiration your body carries out on a leisurely walk
You body is constantly metabolising (converting fuel & oxygen to CO2 and H2O, releasing energy).
Even when asleep, every cell in your body is converting fuel into energy. This is the basal metabolic rate (BMR). Physical activity (including the act of eating itself) increases on your metabolic rate.
When you say 'type', your question might also be referring to whether the cellular respiration is Aerobic (with Oxygen) or Anaerobic (without Oxygen)? In the case of a leisurely walk, your body is most probably completing aerobic respiration as your circulatory system is capable for keeping up with the relatively lower oxygen demand. Rough rule of thumb, if you are puffing, chances are you're reaching peak oxygen capacity of your blood. If this continues your body will resort to burning fuel without oxygen, which has the nasty side effect of producing lactic acid (makes your legs burn after a run).
Another way your body may cope with this oxygen deficit is to make your blood move faster, thus your heart rate increases.
But, unless you are extremely unfit, a leisurely walk SHOULD be less than your blood's oxygen capacity, and you should be doing aerobic respiration in your body's cells.