The only way to avoid being blown up is to follow behind the left one as it walks around the wall, make sure there is always a clear tile between you and the kaboom. Then you can stand in the space below the timer switch until the left kaboom is level with the switch. Take two steps up, stand on the switch, then one step left and follow him round again until you get to the gate, he won't follow you through. This has to be done pretty quickly or the gate will shut and you'll have to go round again, and always make sure you don't get too close to the kaboom.
