There are a few schools that require specifically DO shadowing. But with HIPAA rules the way they are, the busy practices that require more patients per hour due to low insurance reimbursements, personally I think DO specific shadowing is crap and should be done away with. Unfortunately, I don't make the rules.
I would seriously look into each school you are applying to and call them to see if they require specifically DO shadowing. Many do not. Most want to see some kind of medical exposure. I would make some phone calls to each school and ask some specific questions, then look at your options. You may do just as well volunteering in an ER or a homeless shelter or soup kitchen. Run a race to raise money for a local free clinic. Offer to solicit donations of medical supplies for a free clinic (heck, if every doc gave one box of gloves or one box of syringes, that's a big deal). There are options out there.
If your quest is for a DO letter, call every single DO in the phone book and leave a detailed message that says something like "I'm applying to osteopathic schools and they require a LOR from a DO. I would love to come shadow you if possible or just meet and discuss osteopathic medical education. Please call me back if you can help me with the requirements of getting into a DO school." Document every single phone call and response. If EVERY DO turns you down, you should then go to the AOA and the schools you applied to and offer them the documentation of your attempts. If ANY DO offers you his/her time, TAKE IT. Take ALL offers. Bring a CV to any meeting offered and leave it with the doc so they have something to put in your letter.
Every DO knows there are still schools that require a DO letter. To refuse to help a budding student (or worse, an applicant) is a disgrace.