Be aware that soft blade styles without a cage can be very tempting for little fingers to pull on. They won't get hurt if they do it, but the fan will: when my eldest got hold of those as a baby it usually took him less than 2 minutes to tear all the blades off, leaving us with a completely useless fan.
Also, here is my trick for preserving regular batteries: flip one of them. Many of the fans are made so that the switch is easily tripped when stored in a bag or folded against the frame of a stroller. It runs the battery down and then it's dead when you try to use it. I found that the best solution is to always open the battery chamber and flip the polarity of one of the batteries before putting away the fan.