On someone else's aircraft, I've come across a continuous tone when transmitting because the aircraft battery has not recovered to a level where it powers the radio properly after starting. Fitting the radio with a battery charging from the aircraft overcame this short term issue, by guaranteeing a voltage level to the radio.
When the fault existed as described above, it was only on start up; on returning to the airfield after half an hour the squeal would be gone.
However, this is grasping at straws, but worth eliminating.
Is the PAW on the same switch as the radio?
That sounds possible and would explain why the noise had gone away when I got back, however the aircraft has just come back from annual with a new battery.
I have limited (for limited read zero) knowlege of telecommunications, if low battery voltage was the issue, what causes the squeal?
My PAW is separately powered from a battery pack.
Sorry, my explanation left a lot to be desired.
Starting the engine takes a lot out of the battery, and it takes a little while for the charging to get aircraft electrics back to something like 13.8V to 14.4V, even when the battery is new. The low voltage doesn't supply enough juice to the radio, and it howls on TX where there's a large current drain. This is because a circuit in the radio is being run under the wrong conditions to modulate audio on the radio wave. One way to prevent this is to fit the radio, if a hand held, with a rechargeable battery that provides a cushion against drops in aircraft voltage. The radio runs off its own battery, charged from the aircraft but has a cushion/buffer in case aircraft voltage drops.
The easiest way to disprove this theory is to run the radio off its dry cell case with ordinary batteries in it, if the radio does not have a rechargeable battery supplied with it. At this point, the radio is decoupled from the aircraft power, so the fact that after starting, aircraft voltage is not full welly is taken out of the equation. If it still howls, then this is not the reason why.
If the radio is panel mount, disregard all the above.
One other thing to check is that there is no sidetone set on the radio, but this is usually an Icom problem and I think you said you had a Yaesu.