Best arduino for something that is being worn

Simple because using the phone is? And you code well enough to make that so?

Or you could press a button in one place and have a buzzer go off in another without any code at all?

You have different ideas about simple than I do, that's for sure.

If the actuator that "presses the button" is not in the worn device but does have a transmitter then the worn device only needs a receiver and buzzer.

I had the dumb idea that this was for performing in costume in which case thin appearance is everything needed.

So it needs to be smart and have battery, wifi and be tiny as possible.

The ESP8266 WiFi Module is a self contained SOC with integrated TCP/IP protocol stack that can give any microcontroller access to your WiFi network. The ESP8266 is capable of either hosting an application or offloading all Wi-Fi networking functions from another application processor. Each ESP8266 module comes pre-programmed with an AT command set firmware, meaning, you can simply hook this up to your Arduino device and get about as much WiFi-ability as a WiFi Shield offers (and that’s just out of the box)! The ESP8266 module is an extremely cost effective board with a huge, and ever growing, community.

This module has a powerful enough on-board processing and storage capability that allows it to be integrated with the sensors and other application specific devices through its GPIOs with minimal development up-front and minimal loading during runtime. Its high degree of on-chip integration allows for minimal external circuitry, including the front-end module, is designed to occupy minimal PCB area. The ESP8266 supports APSD for VoIP applications and Bluetooth co-existance interfaces, it contains a self-calibrated RF allowing it to work under all operating conditions, and requires no external RF parts.

If you don't need a lot of pins, the ESP can be your controller with builtin wifi. They are very small, have few pins but do have a 32-bit processor that makes AVR's look like slow toys. For less than $10 you get the module and Sparkfun support will get you answers specific to what you have.

Question: how thick can the watchband be? You might fit coin cells there.

GoForSmoke:
I had the dumb idea that this was for performing in costume in which case thin appearance is everything needed.

So it needs to be smart and have battery, wifi and be tiny as possible.

Question: how thick can the watchband be? You might fit coin cells there.

In reference to the size, similar to a fit bit. thinner would be great but thicker is okay. I have two buzzers that are 3V and 5V. the WiFi idea is that because the person who I am making this for is a Grandparent and he lives in Spain where as I live in England. So obviously when they come over to visit time zones are different and that buzzer will go off at a different time. He also has a pacemaker which is obviously the main priority to not mess with or interfere with in any way.