It seems odd to expect to pay for a taxi with any foreign currency (i.e. US dollars in this case). Just try to remember that WE are visiting THEIR country.
Despite what you might think about the current strength of the US dollar, most non-Americans aren't particularly interested in collecting non-native currency. I have visited a few countries with tightly controlled economies where there were active black markets in US dollars and other Western currencies, but that was quite a long time ago. I don't think Mexico is in that category, so save yourself some trouble and just use the ATM inside the Cozumel airport to get pesos. Problem solved. In general, ATMs (and credit cards) give the best rate you'll find (even allowing for the fee for using the ATM machine.)