We taught our son to pee sitting down. Right away. My husband was kind enough to model that for him.
The big toilets can be scary for kids. Especially the sound of the flushing. You can cover the automatic sensors with a post-it (if you carry those around) or drape it with toilet paper. I can't advise you in regard to standing-up... this was the reason we taught our son to sit on the potty first.
I waited until my son was ready (for him it was 3 yr. 4mo. old before I could see readiness... and then we were staying dry all day within a week) and then I helped him up onto the public toilets. I sometimes had to hold onto him to keep him from falling in, and other times, the toilet was small enough. This was for poop or pee. You can also put him in a diaper when you are out and then it won't be a big deal.. when you get home, have him sit on the potty first thing.