No, there's no need to exchange U.S. dollars for Belize dollahs at the airport or anywhere. (If you do, you'll lose a couple of percent in transaction charges.) U.S. dollars are accepted EVERYWHERE in Belize, at 2 BZE to 1 US, though you may get change in Belize currency or in a mix of Belize and U.S. money.
The only reason to change currency is if you can get a higher rate (say 2.05 to 2.15 to 1) which you sometimes can from money changers especially at border areas, but the rate they pay varies daily depending on the demand for American dollars, and for the average short-term visitor it is not worth the effort.
As to fees for using traveler's checks, it varies. Most hotels, shops and restaurants accept traveler's checks at the same 2 to 1 rate, though a few charge 1% or so.
As to the use of $100 checks, that may work fine in a tourist area such as San Pedro or to settle a hotel bill, but on the mainland, at least outside of larger stores in Belize City, large traveler's checks or large U.S. bills can be difficult to change.
Belize First Magazine http://www.turq.com/belizefirst/