Many travel agencies with currency exchange desks simply do not take them. To get rid of traveler's checks you may have to go to a Citibank or AmEx American Express branch. You will probably end up trading in more than you had planned, only to avoid paying the fee again. You will be stuck with a stash of Brazilian cash, and there goes your safety factor down the drain. It may be a good idea to bring some checks for an emergency, though.
Cash Cash is always convenient to bring as spending money.
If you are worried about safety, wear one of those money belts inside your pants until you get to your hotel. Any decent property will have a safety box in the bedroom closet, where you can safely store your valuables. Bring at least a few hundred bucks to pay for expenses like transportation, snacks, and entertainment. Credit Cards Plastic is very popular in Rio, and it will avoid the hassle of carrying too much cash around. Visa, AmEx, MasterCard and Diner's are the most widely accepted, probably in this order.