I don't mind light PDA whatsoever. Hand holding, arm holding, hugs, those are all kinda cute and I think those couples are adorable. Like watching two birds nuzzle each other.
It's when you see people macking on benches that it just gets weird. I don't mind pecks but ugh, I kinda don't want to see people playing tonsil hockey, gay, straight, lesbian, etc xD
As for you OP, I think you should talk to your partner and mention you're scared of doing PDA with them, but if it's something you want to do tell them that. Maybe if you're together holding hands won't feel as scary. Generally, people don't approach you in public for that kind of thing and if they do ignore them or tell them point blank "You are speaking inappropriately, please leave us alone." And if they continue repeat it and add "If you don't leave us alone I will be forced to contact security or the police to report your harassment."
Or just carry two whistles and have you and your partner blow them when someone makes a rude comment to your faces to confuse them and weird them out. A girl in one of my classes is apparently a fashion major and has...questionable taste but it's her own I guess. If people make a mean comment toward her she blows a whistle or a kazoo or starts clapping and doesn't say a word back. I kinda love her idea and tip her a smile or wave whenever I see her now.