seq 1 263 | shuf | sed -n '42p'

for the actual run, if you wish to overdo it ;-)
you may generate an input file with the names of the participants, instead of seq output, in some arbitrary (shuffled?) order. then generate a detached signature for the file, publish only the signature, and invite the participants to submit one random-source byte each. then you concatenate the bytes into a 263-byte file, in the order implied by the input file, and feed it as --random-source to shuf. then you run the command on some bootable live media, publish the input file, the random source, the result, and (hopefully) everyone will be able to verify that you haven't cheated, because they will be able to check that the input file matches the earlier signature, that their random byte is at the right spot, and that the command produces the same output, but they can't cheat in their random byte because they didn't know yet where it would go

picking line 42 is just cuteness ;-)