The lock box idea is an interesting idea. I carry strong side cross-drawl IWB @1 or 2 o'clock (ambidextrous), or in a single shoulder sling tactical gear carry bag.
I have not encountered are ventured anywhere on my bike here in Okieland that I was not allowed to carry....yet.
"There is no hunting like the hunting of man, and those who have hunted armed men long enough and liked it, never care for anything else thereafter." - Hemingway
The greatest ignorance is to reject something you know nothing about.