jremington:
Then your course of study is clear!Like the ATMega328p described in Nick Gammon's excellent article, the ATtiny85 will run for years on a coin cell, using almost all of the same approaches. See the ATtiny85 data sheet.
let's imagine that i can make digispark attiny to consume as less as the 328p, now i can use buttons to send a On signal and an OFF signal, but how i can boost the voltage for the transmitter (12V max, 40mA, <10ms signal send time) ? and then, can i use my 3.6-4.1V arduino to with it ? (XY-FST - name of the transmitter)