Need pins being used by native Timers!

I have an Uno Rev 3, Atmega328P

I understand the native Arduino hardware Timer 0 uses PWM pins 5,6. Timer 1 uses 9,10. Timer 2 uses 3,11.

A shield I'm using makes use of one pin from each of those PWM pairs. However I still need to use a timer. My question: Can I mix and match the PWM pins for one of these timers? Like, reconfigure timer 0 to use pins 5,10 instead of 5,6?

Thanks in advance

The counter hardware is fixed in place.
I suppose the core files could be rewritten to use different timers for millis, micros.
Run into the limits of which are 8 bit vs 16 bit, etc.

I understand the native Arduino hardware Timer 0 uses PWM pins 5,6. Timer 1 uses 9,10. Timer 2 uses 3,11.

TimerX does not USE PWM on any pins. PWM on the pins uses a timer.

A shield I'm using makes use of one pin from each of those PWM pairs.

Why? Using pairs of PWM pins associated with a timer first makes more sense.