I keep my chronograph screens 20' from the muzzle. Even that far out, some of my rifles blast it a bit (30-378, 378, 45-120 NE, and 50BMG).
The easiest set up for your chrony is to get a cheap camera tripod that has the detachable camera mount for it. Make sure you get one that will stand high enough! Then attach the mount to the bottom of your chrony "box". Set up and take down is quick that way and your screen and box will fit back into the original container without a problem. As for the tripod, I keep it in a nylon bag that belonged to a camping chair that broke (cheap walmart). Note to self: look for small nylon bag to put chrony in.
No such thing as a stupid question. What is stupid is not asking it.