I believe that in the 70's ?? Singer put out some models that didn't need oil..a new selling point..this may have been one of them.
You didn't say why you thought it needed oil. If it is running smoothly and not clunking, grinding or squeaking, I would leave well enough alone. Even if you were to get in there and wipe out all of that grease, what's left in the clearances for the needle bar would not allow regular SMO to get in there. If you are adamant that you need the grease gone, it would require taking a good portion of it apart to clean each piece...I wouldn't..I would leave well enough alone.