When we are out and about we use the same potty routine in a public restroom. Except that I usually do the wipe and flush. I use my foot just because the idea of touching the handle with my hand grosses me out. Yes, I do let my kids sit on the toilet. That is why we are really good about washing our hands afterwords.
I have never had one of the potty chairs that fits on the big toilet, but I do have a little potty chair. During potty training weeks I have had two... one for at home and the other one I have in the back of my van for those times when they just can't wait until you find a bathroom. I just pull over and get it out and they can go in the car! It sounds gross, but it has saved me from a wet car seat many times. With boys I could just pull over and they could go just about anywhere there was a bush, but with my daughter... having it in the car was a life saver in a potty emergency!