Michael using that bodyguard was part of his plan to deceive Roth. The bodyguard clearly was a hired gun, from outside the family. If Michael had used Neri or Rocco, he would have signaled Roth that he didn't suspect them of involvement in the Tahoe shooting. He wanted Roth to believe that he was still in the dark. True, Michael at that point hadn't completely ruled out Neri and Rocco as being complicit, but he wanted to prevent Roth from making any assumptions.

As for Fredo: The bodyguard's refusal to shake his hand was probably part of his professional demeanor. The bodyguard had one job--to guard Michael and let nothing distract him from giving that job his full attention. He was probably trained to view everyone else with suspicion, so he shook Fredo's hand only after Michael identified him as his brother.