You could reduce the 100k resistors feeding the diodes a lot, and put a big capacitor from the regulator enable to ground, in parallel with the unlabled resistor.
That will keep the power on for some time after the buttons are released.
If it is a remote control, it is unlikely to be used a lot. A switch mode converter will make it use a lot less power, but only when the button is pressed. Most of the power used comes from what it used in standby, and a switch mode converter won't help at all in standby.
I would also suggest that you run the transmitter from 5 V. It will use more current on 5 V, but it will also transmit much more power. According to the data sheet, going from 3.3 to 5 V increased the current from about 3.8 to 5.5 mA (1.45 times) but the power goes up from +4.8 to +8 dBm, so by +3.2 dB or just over 2 times.
The extra power will make the users have to press the buttons less, so can save overall battery use.