Many people try walking up to Chef Mickey's, but there's no way of knowing whether you'll be successful or not. You might be seated quickly, you might have to wait a long time or you might be turned away. It all depends on how busy the restaurant is. Walking up is a last resort because there's no guarantee that you'll be successful. Will your daughters be upset if they show up at Chef Mickey's and are turned away?
If you definitely want to eat there, it would be better to check online multiple times a day to see if something opens up. If you're flexible as to the date and time you will have a better chance of finding something. You can continue checking even after you arrive at DW. Some people will wait until a day or two before their reservation to cancel to avoid being charged the no show penalty.
Disney's res system has a quirk that makes it harder to find a table for an odd numbered party so if nothing comes up for 3, try for 4 people. If you get a table for 4, just let the CM at the podium know that there are only 3 of you. As long as at least one person shows up for the reservation you will not be charged the no show fee for the one "missing" person.