Go for it !! You’ll never know if ya don’t try and there’s nothing to lose !

How big is the cane that has sported? You might mark that cane somehow (loop of yarn or gardener's ties) and let it get big enough you don't risk losing the sport if a cutting fails.

Is 'Perfect Moment' one of those roses that changes color based on how much sun each bloom is getting? I know there are some roses whose blooms just vary that much.

I agree with ac91z6.... I have always heard, don't try and take the only limb that has sported... but to let the limb get larger so you have more than one chance to make a plant from the cutting.....

Yes, it could well be a sport. And, no, you should mark the cane so it isn't accidentally pruned off, while watching to see if more growth producing that colored flower is produced. It honestly hurts to prune off the only sported piece for propagation, only to have it fail and the sport lost. Good luck!