With some rolls there is a larger core with a 1-inch hole in the center; in which case you can add a cylinder, 1 inch in diameter, 1-3/8 inches long, and bored to accept the axle in your loader. You get one of these at the end of an Ilford roll.
I haven't seen a roll with no core.
Fuji came on a spool with large discs on each side to contain the roll.
If that is the Arista Edu Ultra it does come on the larger black core that accepts 1-inch diameter inserts.