In either case, there's something missing — or maybe it's because the sentence is out of context. Just to say someone washed his hands like a surgeon is insufficient; you need more detail. "He scrubbed his hands for over two minutes" or "thoroughly" or "with meticulous care" like a surgeon etc.
They do have different effects. The first one puts your character first. The second one creates an image which the reader then has to insert your character into. But I'd need to see more to tell you which one works.
ETA Okay, now that I've seen your context, the second example absolutely does not work at all. You cannot connect "pouring an ingredient" to "washing hands like a surgeon." Sentences attach to what comes before them as well as to what comes after them, and if your sentence starts with a simile or an image, I'm going to think it's a continuation of the thought or the sentence I just read unless you give me direction to do otherwise.
I thought it was going to be more like:
Time slowed to a near-crawl, like it always did when he was lining up a shot. He aimed through the two windows, finding the spot just above the cabbie's heart to allow for the bullet to fall with distance, and then fired. He was gone down the hall before the echoes stopped ringing.
His new flatmate was safe. Now he only needed to clean up the evidence. Like a surgeon after an operation, he washed his hands thoroughly. The gun disappeared into the murky waters of the Thames. A quick brushing took care of any glass splinters on his coat, and then he was off to wait outside the police barrier for the DI to finish with Sherlock.
See, that puts your simile into context which works no matter where in the sentence it lands. It's supposed to emphasize how clean his hands are, but it also links backwards to the previous sentence and its events (that the shooting was quick, clean, and preicse).