It's probably a throwback to his early years, when as a considerably larger gentleman than he is now, he used to perspire considerably during his energetic performances, and needed a hankie to wipe his face at frequent intervals.
I imagine that now he is older, slimmer, and possibly less frenetic, he doesn;t need the hankie, but it is something of an identifying symbol, so he keeps it going.
This is an educated guess, rather than a known fact - if i catch up with him, I'll ask, and post here.