Data firing at Fajo was a terrible decision. Fajo was unarmed and in no position to threaten Data. Data should have been courtmartialled.
By no stretch of the imagination was Fajo 'Unarmed'. He wasn't holding a weapon at that very moment, but the power he had over Data and his own crew is a form of armament.
He had no other means to harm or coerce Fajo available to him at the time. Also, since Fajo had all the access codes and nobody else would dare disobey him, no other means to escape. His options were literally, kill him or surrender to him, arming him in the process.
And Fajo had unlawfully imprisoned, enslaved, and declared war on Fajo.
Now, had Data known that the Enterprise had found him, then you would be correct, but he had no way to know that.