Are you really supposed to swirl Champagne?
No. But do not let me stop you. Just be cautious in that day apparel if the flute is too high.
You need to avoid swirling mainly in order to maintain maximum carbonation — the very small bubbles you paid so handsomely for. Can a quick swirl or two mess your wine? No. I occasionally make a point of swirling sparkling wines that I find are overly fussy to start with, just to smooth them out to a flatter and more sippable state.
With wines, the purpose of dissolving is to get the liquid to scale up the sides of the glass, thereby increasing the evaporation surface to be able to amplify aroma. With sparkling wine, that is not quite as crucial because effervescence does much of the air-lifting — so to speak — for you.