^I agree with those statements.
It felt just as awkward for me to do, but I assure you, it won't come as a surprise to the doctor you're shadowing when you finally ask. Chances are, if said DPM was smart enough to finish Pod school and residency, then said DPM is smart enough to know you need a Letter of Rec for entrance.
But I really must follow with this, though:
-When I interviewed at my school, I was immediately told of my acceptance. Then, both, the clinical and basic science interviewers recommended something that will shock many a pre-pod: "You should shadow some more podiatrists. 'Get a grasp of what the profession has in stock for you now and in the future."
-The truth is, shadowing a podiatrist was (and continues to be) as educational and downright fun an experience as can be for me. I'm done with my first year and still look forward to spending a good part of my next vacation doing just that.
-Point being, the doctor you are currently shadowing knows you are limited of time with grad school applications and current (if applicable) course-load. But I'm certain that if you ask for a letter of recommendation it will not stamp your welcome to a close. You could even get it over with on your first handshake and introduction. In the end, there's a true and purposeful benefit to shadowing a doctor in the profession for which you're applying. And that's probably why such is the standard requirement in every professional school.