I just use a broom stick. It does not matter if the core of the tube is filled by the shaft. If it is smaller it will not unroll as easily, and in this appplication that is what you want.
In the past there were things called roller easels, that basically had a feed of paper on one side, and a take up on the other side. You printed the size of the mask, and set the paper advance setting to match that mask size. mask size was variable. Some masks were rotatable, and the easel slid on ball bearing into grooves with detents, so you could say print 2-5x7's most efficiently on a 12" wide roll. Motor advance and paper gate open and close coordinated with the advance buttom when you were done exposing that part of the paper.
Most custom print shops pitched these devices a half decade ago. They are kind of big for home use. They take the roll of exposed paper and feed it into a roller procesor and prints were pulled at the end after the roll was cut up. You can see how having an analyser, having it calibrated to your process, and an operator to know how to position the probe and set the channels was kind of important to the use of such a device if you have ever printed color.