If the damaged tyre is the front one, switch it with the rear. A rear blowout is far less risky than a front one.
Although I would agree with
@Slick that a tyre boot is for getting you home, not for going out on.
On the other hand, the rear tyre carries a much bigger load than the front one (I once put my bike on two scales to then sit on it, the front indicated 20, the rear 85 kg. I have to replace (due to wear and flats) a rear tyre 6 times for every 1 front tyre.
My front tyres surface is full of carves, and when I check tyres for objects I find these only in the front tyre.
Because at the rear, much sooner, they're either pressed out either puncture, due to the much higher load.
A long used front tyre that suddenly has to carry a triple times as big load, likely doesn't need much more to blow out even without any exceptional damage event alike a tear due to a metal strip. Both together appears to me like a sure soon failure.
So I'd rather keep the front tyre on its place instead of swapping it with the back.