Is it permissible to say: "My father, there is none like him," intending to negate any resemblance to him in his attributes and fatherhood, knowing that Allah Almighty is described by His saying: "There is nothing like unto Him"?

There is no objection to describing the father with the aforementioned phrase. Speech is interpreted according to its correct meaning Islamically, not its opposing one, especially if the context and indicators point to the intention of the correct meaning.