I understand. But the OP didn't mention that so that's why I had asked.
In "my" recent situation, for example, there was no p-trap plug to remove; so I went through the outside 2" access pipe; yet, to actually *snake* the kitchen drain, would have taken a much smaller diameter than your typical snakes are, because of the way a kitchen drain is designed (so that stuff doesn't go down it, I guess).