You can't do either from the airport. Cheapest is cancun-discounts.com for a shared shuttle. Not sure who is cheapest for a private shuttle for one.
But they are cheapest for a shared shuttle. You can always taxi back but still more expensive and if you do that, cross the street, taxis always more expensive in front of a hotel. Do not pay more that $30 for a taxi and settle on price before you get in.
Cancunshuttle - Cancun Airport Transportation pretty much $50 round trip, private. we've used them 7 times now without any issues.