Choosing voltage regulator and battery for a compact RF remote control (transmitter)
TWS-DS-6:


  Supply Voltage : 1.5~ 12 V


ATtiny85:


  
  Operating Voltage
  – 1.8 - 5.5V for ATtiny25V/45V/85V
  – 2.7 - 5.5V for ATtiny25/45/85
  


I wouldn't bother with a regulator. Assuming the transmitter doesn't use a lot of power, I'd use a CR2025 or CR2032 directly.