I don't know about that. While of course not capable of actually committing murder with his own hands, surely as a member of the Corleone Family for virtually all his life, Tom would have no trouble acting upon such an opportunity. I always note the way he coldly and callously explains to Geary that the girl had no family and that it would be like she 'never existed'. And the delightfully evil gesture of wiping his hands as if to say, 'That's that...!'

While of course there may have been a discussion with Michael on a way of getting Geary in their pocket...I think that once he was named Don, Tom could certainly have ordered the girl's murder to get to the Senator.

After all, she was 'small potatoes'.

Apple