Takina should just use the non-lethal gun and shoot Yoshi, get the heart, and have it transplanted into Chisato. AFAIK, the heart itself is what is special. The surgery itself doesn't need Alan level skills.

I still have no idea why they can't just give her a normal human heart from a brain-dead donor. I know those are hard to find, but it's like they didn't even consider it.