3 terminal 5V high side load switch with 3.3V control
A PNP transistor can work, but will need a base resistor.  You gave lots of info about the load but not the worst case current draw directly.  Apparently that is around 300 mA.

Let's say the minimum guaranteed gain of the transistor is 50, so that means you need at least 6 mA base current.  With the emitter at 5 V and the microcontroller output at 0 V, the drop on the base resistor is 4.3 V.  Aiming for 10 mA base current to have some margin, 4.3 V / 10 mA = 430 &amp;Omega.

I know you say you don't have pads for the resistor, but that doesn't change what the circuit needs.  Mistakes happen in early prototypes.  Cut a trace, lift a pad, or whatever to allow the resistor to be inserted in series with the transistor base.  Fix it right next spin of the board.  This is why you make prototypes.  Editing prototypes with a few cuts, jumpers, and flying parts is normal business.