So let's take this scenario a step further. You and your partner have left your car and you are loaded with emergency preparedness equipment in an unfamiliar urban area that turns out to be, "not the best side of town". There are thousand of people trying to get places, in vehicles, on bikes and by foot. How do you proceed on foot through an area where there may be potential looting and/or theft? Do you travel back streets and alleys or stick to the main streets? What would you do to fit in or to become a chameleon?
Me, I'd try to look homeless and crazy. i.e. no money, and nothing of value. Play the part. Keep repeating a phrase, like "Box 3436. I must get there soon!" If someone tries talking to you, just unload (not the weapon!) "I must get the Rubix cube into Post Office box 3436, the world depends on it! I have been sent by the great Roknard, and he has communicated to me the importance of this mission, and has infected me with a contagious disease to ensure that all those who interfere will die a horrible death. Rocknard said that this disease would infect only those who wish to do me harm. If you leave now, you will be safe. Do not let the Curse of Roknard be your undoing". If they still seem interested, uh, maybe they're mentally ill, and you're going to want to move away, and prepare to defend yourself.
This is what I try, you're mileage may vary, and only attempt this if you are properly trained. I have no clue whether it would be successful.
The unfortunate reality is that homeless people, and especially homeless with mental illness are ignored by society. I would expect that they would be ignored in a disaster, no matter the neighborhood. The only problem you would have would be racism. Someone else will have to figure out how the handle that, I don't have a clue.