I can tune my E down to D in about two seconds without a Drop Tuner. I have had to do this a billion times in my not so short "career". Happened to me a lot in my days, seeing Drop D tunes on lists. I got very good at it over the years. Because I practiced doing it. Along the way, I acquired the taste for Low B strings. So, today, I rarely tune for songs in lowered tunings. But drop D songs such as Sober, 46 and 2, Unchained, Slither, and a couple others are still more effective with the Drop D. So, I still, on occasion, have to use the ole acquired skill of tuning my E to D and back, if only so I don't add further difficulty in writing set lists, or hold my band(s) up in any way on stage. If you practice this for a few hours, I'm confident you'll be able to do it with a minimum of wasted time. And it's one more arrow in your quiver that sets you apart when bands are hiring or need a sub.
Of course, as suggested, there are floor tuners that mute when tuning, or mutes on amps while you use your headstock tuner. Those are quite effective. But I can tune faster than the steps it takes to use those techniques, just using harmonics to tune and my ears.