Also, don't mention that you want to shadow because it will make your application look better. Maintain that you want to shadow for your own benefit and because it will help you in your personal application process. I just had one of these types of interviews with a DO that agreed to let me observe her surgeries for a few days and I never once said that I needed an LOR, or I needed to shadow to help my application. She asked me about MD/DO and I told her I've shadowed MDs in the past, but am interested in DO as well. I explained that I was applying to both sides since my primary goal was to be a physician, and that I was considering DO because I find OMM/OMT and the overall holistic approach to be interesting and beneficial. All of that is true, but it's also true that I need more shadowing hours, need a DO LOR, and need more patient interaction for my application. I didn't mention any of that though.
Also, you don't have to lie and say you are interested in OBGYN if you aren't. But don't say that you aren't interested in it. It's perfectly fine to have an interest, but it's also fine to have no clue. The DO I'm shadowing next week is a Dermatologist that specializes in skin cancer and skin cancer excision. It was a really strange coincidence that I found her and she agreed to meet with me because my first specialty interest was Oncology, and lately I've been getting interested more and more in surgery (because of A&P class). I'm interested more in ortho than derm, but I didn't say "Oh I'm not really interested in derm."