I have an older 1" (25.4mm) carbon fork from Nashbar. The inner diameter of the carbon steerer is 20mm at the max. My two options are to use a 1" compression plug or a start nut, but I need some advice.

Since the steerer is carbon, I have always been under the impression that a compression plug is better, versus using a star nut for a steel steerer. Is this thinking wrong?

Should I use a compression plug? I am trying to search for ones that are 1 inch but it has been tricky.

I also have some star nuts that are for 1-1/8th forks, but I am hesitating before hammering them in the carbon steerer. That seems like the wrong thing to do. Should I use a 1" star nut?

pics below. thanks

Inner diameter is a maximum of 20mm