I haven't bought a Ozone preroll in a long while, but you can get all sorts of doob tubes on Amazon
These are similar to ones I have seen at IL Dispensaries
For reference, the cardboard tube that they include inside of Raw 1 1/4" cones is ~65MM and for the king sized Cones is ~95MM. Sorry, it was a reference I thought most stoners could compare too :)
Your "mini" maybe 98MM. A king sized Raw cardboard tube barely fits in there, but it fits.
Heres other options