The East face, AKA the contraforte, is high on Corcovado and contains some shorter climbs and single pitch climbs that can be done in a few hours at the most. 

The crux of the approach is how to get to the parking. A cab or Uber is usually the easiest, but mind that you're done with your climb well before dark as most Ubers don't want to pick you up late, leaving you vulnerable to be price gouged by a cab. 

After solving the problem of how to get to the parking area, the approach is very easy by Rio standards! Take the trail from the visitors center (just downstairs from the two little cafes with outdoor seating) for ~5 minutes. At one of the switchbacks, keep an eye out for a faint trail continuing uphill towards the telerifico tracks rather than taking the well trod switchback trail. This climbers trail will spit you out at the telerifico where it passes extremely close to the road. Walk the road until you reach a switchback with K2 scratched into one of the stone bollards. Here there's a trail into the forest that passes many climbs and terminates at a ridge with a small clearing. Continue downhill from the clearing for ~40ft to reach the base of K2!