Because there's a good chance her condition resulted from him trying to strangle her in the first place. He's probably a Scott Peterson who didn't succeed the first time.
You all may be exactly right. Then again, there is another wrinkle. Apparently, he wants her body cremated. My understanding is that under Florida law, an autopsy is always performed before that's done. If he didn't want anyone to know, why would he risk having something done that has a chance of revealing what happened to her?