I rolled into a prof's office straight from work, smelling like a petting zoo (yay animal research! ), and asked him for a LOR pretty please. We chatted for a bit and I apologized for looking/smelling like a monkey. He said "Oh...well it's not that bad."
Moral of the story: if I can get a LOR literally smelling like ****, you can get one while wearing a sweatshirt and jeans.