Just wanted to weigh in...
I don't think an armband is an awful idea, especially since there are a number of nice waterproof options, BUT I find it to be a pain to truly use it when I've got it on my arm. It's one thing to have it up there to switch songs, but it's an entirely different issue to take a call or text IMO. Our local temps/weather are very similar to WDW's and I've never found it to be too hot...just a pain if I want to use at as anything more than a glorified iPod while exercising.
A slim wristlet isn't a bad idea. When we were at DLR, I used a snap wristlet for our park tickets. Kind of like you get used to the feeling of a watch on your wrist, you get used to the feeling of the wristlet being there and just how heavy it should be...so, it's a constant reminder that your phone should be there. Some also have little pockets inside...so it's decent for multiple purposes (i.e. some cash, gift card, etc.)
The best option, IMO, is a crossbody bag. The pics are LeSportsac ones...which I picked because they handle water a bit better. Not saying you want to go throwing them into the water at PotC, but I'm usually comfortable with taking stuff in one of these bags on something like Splash and they're a little more, well, sturdy than something like the Dooney wristlet above. The Dooney is a good bag, but the leather won't like water as much. In any event...these are some ideas for crossbody bags. With a bag, you just get so in the habit of taking it in and out that I think it's less likely to be left behind (compared to people who put them in their pockets) and they are pretty secure with all of the zippers in a bag like this.
My older one is about a year and a half away from her first phone, and while she'll probably get my old HTC Onc X handed down to her, I still don't want her to go losing it. These are the kinds of things I'm looking to for her in the parks come the time.