If you can't answer these kinds of questions on your own, you might want to consider another line.what if they are not there for you, or for something thats happening in the neighborhood, and they knock? do you still not open the door and talk through it, risking unessessary suspicion? can you open it a crack? like some little girls lost or something. you'd be an asshole right?
I think the big problem with most in, er, "non-traditional" lines of work is that they're underqualified.
No, you don't open the door. Talk through the door. If you can't come up with an excuse...? How hard is this? You have a nasty flu, you're naked and exercising, you're having sex, you have social phobias.
STOP MINDING WHETHER YOU'D BE AN ASSHOLE. That's the first thing that has to go out the window when dealing with cops.
EMBRACE YOUR INNER ASSHOLE. Become one with him. Say it in the mirror until you believe it: "I am the world's biggest asshole." And no, that doesn't mean verbally abusive, violent, or profane. Cops love it when you curse, use foul language, or confront them physically. Makes you a nice guy in their book, because now they've got you.