There's no choice, no room for hesitation. Not removing the shrapnel means barely hanging on, while taking it out offers a thirty percent chance of survival. Of course, it's removing the shrapnel.
Albert and Andy He were called for help in the end. If they were in charge, they certainly wouldn't waste precious time, but Yang Yi and Satan weren't life-and-death brothers after all. So, when faced with a life-and-death decision, they had to clarify this.
Yang Yi made the choice, now it's up to Petra's fate. This is what destiny is all about, the destined can't live, and those meant to live can't die. It's all left to fate now.
Yang Yi believed Petra wouldn't die, as he promptly provided effective first aid to Petra. Anton Hai also brought the person most likely to save Petra from all of New York. Since the first two steps went smoothly, then the final and most crucial step won't have any issues either.