Yes, you can use the processor to control the power. The NPN driving a PNP will work and reduce the current draw from the processor digital pin. The idea is ok, just more than needed.
A single P-channel mosfet that is adequately rated to carry the operating current can be driven by a digital output. If the gate of the mosfet is pulled up by a largish resistor, the transistor will be normally off. The processor would hold the gate low while it needed power then raise it to turn off the power.
The power button will need to be held on for long enough for the processor to initialise. People are slow but variable. 10ms - 100ms on a button might be ok.
Do some experiments, find out how long the power stays on when the button is pressed and released. Look at the code and get the HOLD signal active as soon as possible.
Maybe a large capacitor would hold the supply up long enough after the button was released for the processor to get control.
Measure the supply current and voltage and check the voltage needed for the regulator and then calculate the size of a cap needed to supply that with acceptable voltage drop in the time available (I=C*dV/dT).
If the radio isn't needed immediately, a similar arrangement could be used to turn it on, reducing the turn on current so a cap would be more likely to work.
Have fun. Let us know how you get it to work.
Pogo