Fitting 4pin female in 3pin male

I think you are good, no danger.
4 pin fans are designed for PWM control.
That is cycling the fan on and off.
But, they work perfectly well in a 3 pin header but at full speed.

A 3 pin fan has a + and a ground pin, usually black and red.
There will also be a yellow lead which is a speed sensor.
Your fan controller will adjust the speed by adjusting the voltage across the black and red leads.