That's the exact type of setup that I used for ten years except that the small diameter end of the stopper was pointing toward that outside of the cooler. If you push the stopper into the hole from inside of the cooler with the small diameter end pointing toward the outside of the tun, any pressure inside of the tun will merely make the fit tighter. The stopper can pop out with the tun filled with hot liquor the way you have it configured.