So, after the "oily hair/silk suit" rap, Michael probably turned to Tom and Neri and said, "Nail his ass the next time he shows up at that brothel."
Nah. He would have said. "You know about Geary's dalliances? You know he is a regular at Fredo's place?" To which Tom would reply, "Who should I use, Rocco or Neri?" And Michael would reply, "Neri. This will involve drugging the senator and brutally killing a young girl who has no involvement in any of our business. Neri is the more brutal one."
I think the prostitute was drugged along with Geary, given that many other people were in that brothel, including in nearby rooms. The last thing they'd want would be for people to hear her screaming.
Also, while she certainly wasn't a gangster, I don't think it's completely accurate to say she was completely uninvolved in the Corleone family business. One of their activities was prostitution, and she was a prostitute who worked at one of the brothels.
