IMHO,Fredo would have been a dead man either way. Mike knew about the betrayal in Cuba,so the boat house scene,while poignant,didn't result in Mike suddenly deciding to kill his brother.I believe that Mike made the call much earlier.

To make my case,I am going with a few assumptions that I think are feasible.
One,in the overall Mafia community,the news of Fredo's treachery would get out to the other Families.
Two,Mike's rep would suffer by having his own brother go against him.
Three,the Corleone's would be seen as a Family beset by internal problems,hence a possible takeover target.
Four,Mike himself would be a laughing stock.

Given Mike's general ruthlessness,and his twisted enjoyment of his newfound power,he saw no other option than to kill Fredo,knowing that regardless of the official version,the people "in the loop" (both friends and foes) would know damn well that Mike killed his own brother.

In Mike's mind,this was the sledgehammer move,much like the totally unnecessary hit on Roth at the airport.
His only concern was to show the (under)world,that the Corleone's,like the Bochiccio's,would not leave any insult unavenged,regardless of the consequences,and that Mike was not to be crossed by anyone.