Your receiver micrf211 has a typical supply current of 6mA and shut down current of 0.5uA. For example, if you listen half of each second, you can limit the average consumption to half (3mA). Let's assume your transmitter sends a packet about 50ms duration, and retries it while the key is pressed. As suggested before, if the users can hold the button for 1 seconds at worst this can work. 50ms is within 500ms.
This is from datasheet of nrf52810 which I use occasionally for BLE projects:
Radio transmitting @ 0 dBm output power, 1 Mbps BLE, Clock = HFXO, Regulator = DCDC --> 5.8 mA
Radio receiving @ 1 Mbps BLE, Clock = HFXO, Regulator = DCDC --> 6.1 mA
Sleeping, System ON, Full 24 kB RAM retention, Wake on RTC (running from LFRC clock) --> 1.5 µA
The ratio between reception and sleeping is above 1000 so the key point is sleeping when idle.