I have worked in financial services for my whole career. You will find credit cards widely accepted, especially in tourist destinations like Cozumel. You will also find US currency quite popular, so if you simply take some cash with you, you will not have a problem having it accepted.
The fees on credit cards and cash machines are reasonable. Where you will get taken advantage of is on foreign exchange.
When you start swapping one currency for another, you find the price works against you in both directions. You want to minimize swapping from dollars to pesos back to dollars. Fortunately in Cozumel this will not be a problem as you will find the dollar accepted everywhere.
Take your credit cards and an amount of cash you are comfortable carrying. Then enjoy your vacation!