That's fine. You have that choice. I only visit immigration once a year so there's no value for me to carry it. I just print it on the one day I'll need it.
You can probably take a chance yourself and go solo, but as Ron Angel has said, the border/visa run companies will not take you, as there is no guarantee you won't be arrested
See if the airlines have an interlink agreement. This way you can get your luggage checked through to the destination. If not, you will need to clear immigration, then pick up your bag, clear customs, make your way up to the top level and check in for the second flight. As a safety buffer, allow three hours for this process