Getting home to your family every night is the important thing.
You seem to know your way around firearms, so I would say go ahead, and just keep it to yourself, and don’t flash it around everywhere (obviously). I would take care to not carry in the attic, as this would be awkward and may result in an ND (Negligent Discharge). However if you have one of those small toolbags with the CC compartment, or some of the CC shirts from Under Armor then I would say use those.
Obviously you dont want to carry a Desert Eagle, so that being said I would carry a more compact sidearm if at all possible.
As far as a realtor (which I wouldnt worry about, a lot of them carry as well) or client finding out about it and getting all “baby killer” on you, expect it to one day happen. In that case, remain calm and explain to the client why, and show him/her your CC card to at least give some assurance of responsibility. If they are still bent out of shape about it, then you may have to void the deal.
As long as you arent trying to be a crime fighter, you will know when and where you should carry, and when and where you shouldn’t.
IMHO I have been in areas that I wouldn’t even want to get out of the car, let alone do an inspection. But like Paul said, if the neighborhood is that bad, then don’t do the inspection. No amount of money is worth your life.