Nope, no chutes. Nowadays, there's stunt people that will do wing-walking but often have a "slim-line" chute under their outer garments. But, there are still true wing-walkers now.

But, there are differences also these days. Most of the barnstormer acts of the '20s-'30s were done in fairly "straight & level" flights. The old Jennies & similar planes that had wings big enough to walk on & necessary handholds, didn't have enough h.p. or weren't constructed well enough to do full aerobatic routines at low levels. But, there have recently (relatively speaking) been acts such as Johny Kazian who would actually do an untethered (& no chute) act of wingwalking. He & Jimmy Franklin were an unbelievable show together. But, different than the acts of 80 yrs ago, Johnny (& other more contemporaries) would do this often while the big Stearmans, Wacos & Ag Cats (Franklin's plane) were wound up doing loops, rolls, & spins, within a couple hundred feet of the ground. If they got higher than 500', the crowd would get bored now & go home.

http://www.icasfoundation.org/hall_fame/2004/kazian.htm

However, I still marvel at what that lady was doing 80+ years ago. I'm sure her training was almost nothing.