Don't give it much thought. I grew up in Maryland and have spent vast amounts of time in DC and never once had a bad encounter. I was just there last July and I took my daughter into DC to do the tourist thing for the day. Granted it was not her first trip to DC you can't do all the museums in a single day and speaking of museums. Entry to most is free but DO NOT EAT at any of them. They charge an incredible amount of money for a basic meal.
While you are visiting the mall area you have very little to worry about. The memorials, reflecting pond, etc. you will be fine. I didn't give the thought of not being armed any thought at all. I was having too much fun enjoying the museums. My favorite is the Air and Space Museums and sitting on the steps of the Lincoln memorial to do a little people watching is a must.
Enjoy your visit, don't stress about not being armed. You are not going to wander into Anacostia or any of the other bad parts of DC by accident. DC is not as bad a city as it is made out to be. The crime/murders you read/hear don't take place on the mall very often.
BTW. Be very careful what you carry. You have to pass threw security check points entering the Air and Space museum. They do have metal detectors and they do check baggage. I don't remember if the Natural History museum had them or not. It is hit or miss but you could be denied entry if you have a knife. I would visit the web sites of places you are going to visit to find out what is legit and what is not.