A week before you hit the pavement, take a day to properly research and set appointments with both no-fee apartments and 1-2 brokers from different brokerages. Take the first day to go through all the no-fee listings, make sure to make a list of all you have seen. On the second day, bring this list to the brokers so they don't take you to something you could and have already seen on your own. Because, once a broker shows you an apartment, even if you could have found the apartment on your own, your bound by the disclosure form you sign to pay them if you rent an apartment they've shown you. 

If a broker takes you to an apartment you could have seen on your own and you missed it in your research, that's just the way it goes sometimes. The broker doesn't get paid unless you sign a lease and they are taking their time to take you around and show you everything you requested. Hopefully you exhausted every no-fee lead before you meet with a broker, but it happens! Suck it up.