How to change a command line argument in Bash?

You have to reset all arguments. To change e.g. $3:

$ set -- "${@:1:2}" "new" "${@:4}"

Basically you set all arguments to their current values, except for the one(s) that you want to change. set -- is also specified by POSIX 7.

The "${@:1:2}" notation is expanded to the two (hence the 2 in the notation) positional arguments starting from offset 1 (i.e. $1). It is a shorthand for "$1" "$2" in this case, but it is much more useful when you want to replace e.g. "${17}".

Optimising for legibility and maintainability, you may be better off assigning $1 and $2 to more meaningful variables (I don't know, input_filename = $1 and output_filename = $2 or something) and then overwriting one of those variables (input_filename = 'chintz'), leaving the input to the script unchanged, in case it is needed elsewhere.