But if you are the type of foul miscreant who sits around fantasising about such a prospect, then you need fantasise no longer.
For Savage is one of a host of bald-lipped advertising luminaries who have donated their time and energy and donned facial hair for a new campaign designed to raise a bit of dough for charity.
Savage, John Hegarty, Mark Wnek, Peter Souter, Tim Delaney and Nick Bell are among the big nobs who have contributed to the Tacheback project, an initiative designed to boost the coffers of the male cancer charity Everyman.
The creatives all appear in a viral appeal, which urges members of the industry to sponsor their colleagues to grow big moustaches. And, keen to practice what they preach, all six of them are sporting flamboyant 'taches of their own.
How well they all scrub up. Hegarty looks like a new man - hands up who thinks he should have worn that moustache throughout his career? Bartle Bogle Dali has a good ring to it, don't you think?
Meanwhile, Bell, newly installed at J. Walter Thompson, urges the community from beneath a big, brown, bushy brush of his own to prove wrong the "snipers who regard us as over-paid chancers who own more Calven Klein underwear than we know what to do with".
Cue Mark Wnek. "All right, maybe we are," he concedes.
The star of the piece is undoubtedly Tim Delaney, who models a little Hitler-styled square 'tache no bigger than a postage stamp. The company behind the viral, Hotspur & Argyle, tried to convince him it was a Charlie Chaplin-style moustache, but he wasn't fooled.
The most uncompromising and exacting man in the industry made up like a dictator is an image that will delight some, while reawakening some awful, harrowing memories for others.