If you set the screen up 20 feet or so from the muzzle of your gun, you generally won't have any problems with patches. A Heavy felt, or OP wad may go over the screen, however. Consider substituting a loose filler, like corn meal for these sessions with the chronograph. They won't travel to the screens. The same happens when hornets or wasp nests are used as a filler.
And, if you try Jim Rackham's suggestion of using OS card instead of OP wads, and poke an off-center hole in each OS card, the cards will separate and flutter to the ground within that first 15 feet.