Refractors are a good idea, yes. When I do (did) sidewalk astronomy I always take a frac and a Newt or Cassegrain. I agree that fracs are what most people associate as a telescope. But if the main reason for my session is a personal one, not an outreach one, then of course I take what best suits my needs.
Unfortunately we as astronomers need to work with the general public's ignorance. It's not putting down the public but a statement of fact. And it is our responsibility to work as favourably as we can as situations present themselves. If someone calls the cops, we can't help that. What we can control is how we speak to the police.
And even if you have a frac set up to show people the Moon, of those that walk away many do so because they are suspicious. Suspicious that you are trying to sell them something, or makes a fool of them, or just mistrust that you won't hurt them somehow
What's funny about many of these people as well is if they see a crowd of people around you with a buzz of excitement and looking through the scope, many of these folk who would have walked away would actually stop to have a look themselves!