I don't think a PGY2 letter is going to be much help. Beside if you are shadowing a surgery resident, how are you not interacting with the surgery faculty enough to ask them for a letter? As a general surgery resident my students and I are always with faculty in clinic and OR. Usually if you worked really closely with a particular resident they can give some specific input to the faculty. Also my chiefs dont write letters either, they usually just give input to the faculty.
Now if you mean that this particular resident is the only DO in the program, well IDK what the point of the letter would be. I am not a DO but when I did apply to DO schools, my understanding was that a DO letter was supposed to show that you have experienced some osteopathic principles. If this is a DO TRAINEE in an ACGME program in a field is historically anti-DO, I agree with FrkyBgStok (I would blow off the LOR).