I've heard of kids from cities being given money so they always have something to give a mugger instead of looking like you're holding out, I don't go that far but I remember it to keep perspective.
I recently made an effort to carry cash with me so I can leave tips in cash, still working on that. Would you be open to keeping singles on you to give? You can even give max of one per excursion and then decline or ignore the rest or any combination but maybe having that as a plan can help you feel comfortable. Yes you're training yourself and it's because you deserve the benefits of training.
As for non-bums hello is good, also fist bumps and nodding upwards; that stuff is cool AF and make people so damn happy.