I would use 'one times one is one' I understand with the singular number 'one' it would be confusing but regardless of the value being multiplied 'times' is always used.

I agree with Lance, except that "one multiplied by one" is not more clear. If you say [number] times [number], there will be no confusion. As he said, for multiplying numbers you always use "times."

"One times one" The "times" you are currently referring to, is "multiply/multiplication" （成法）, not "occurrence" （次数）. For multiplication, you always use "times". Though to prevent confusion, you might want to use "one multiplied by one" instead.