No switch is involved. The chap-stick used is fully functional. If you want to hand out the chap-stick there is a very natural, clever way to get rid of the gimmick so that you can do so. This means that you will start with the gimmick ready and you have the option to end clean. The bill can be borrowed and the bill and chap-stick can be handed out at the end.
As far as the penetration goes. You can push the chap-stick a bit further than the cap without a problem, then change directions and pull it back out. You cannot push it through one side and pull it out the other.