Thanks for the ideas. I know RF or IR would work, but then I would need a control unit at the firing line with a display, switches and audio capability which would more than double the complexity and size of the overall system. I want it to be as small and simple as possible. I figured the smart phone already has that capability.
I don't think I want peer-to-peer, but I don't really know; I envision the phone sees an open WiFi network, connects to it and navigates to a website. I guess I am trying to find out if an Arduino (or Teensey3 or mbed or STM32 or ???) and a WiFi shield can act like a network controller and web host (not sure if my nomenclature is correct).
I had to look up Class 1 Bluetooth. I am not sure my phone (which is probably only class 2) would be able to reach that far. With my (probably) class 3 headset it can barely reach 10 feet, but it's worth looking at. I have considered connecting to a box with bluetooth and then to the target with RF, but it would still be another box and battery.
I regularly use my phone to play MP3's of the range commands. There are ear-muffs with audio input, but mine are now broken, so I snake the ear-buds under the ear-muffs. It works fine.