I know it will sound a little snarky, but avoiding getting shot is a great way to not have constant issues with oil on the goggles.
I rarely see the oil effect anymore. I actually credit the beta Career for that. When it first came out, I couldn't keep a pilot alive for more than one week. I looked carefully at my decisions on when and where I engage the enemy and modified a number of things to ensure I would stay alive and that I would only get into fights when it was to my advantage. And, when I get bounced, I prioritize escaping and establishing an advantage before going offensive. Now I can have a career last months. And I fly Dead is Dead, which just reinforces treating your virtual life with care.
You mentioned head ons. Start by not getting into those situations to begin with. Once your engine is spewing oil, you have very limited time until it dies altogether, so spotting and targeting other aircraft is no longer the priority. Getting safely down to ground on your side of the lines is.
But to answer your question, the game doesn't provide a way to use the scarf to wipe off the goggles. There's debate over how effective that would be anyhow as it most likely would just smear the oil. It would be a cool effect if you could wipe them though. It would remove the majority of the splotches, but leave a smeared film that should still distort your view a bit. Of course, even after you wiped them, they would get splattered again until your engine died or you turned it off.