Presston, if you will be there from daylight to dark daily to re-open the cone when it collapses and closes, screen will do. Otherwise, 1/8 in. hardware cloth.
Many beeks have scraped hive bodies making holes in them for the cone. Most are on the scrap heap now. Just ask Robo. That's where his is. By the time the queen comes out, the catch box will be queenrite, so no place for the tree queen. The fight to follow may just get them both killed.