Using quotes for i in "$(cat $1)"; results in i being assigned the whole file at once. What should I change?

Bash doesn't do word expansion on quoted strings in this context. For example: $ for i in "a b c d"; do echo $i; done a b c d $ for i in a b c d; do echo $i; done a b c d

Bash (like all Bourne shells) has a special syntax for referring to the list of positional parameters one at a time, and $* isn't it. Neither is $@. Both of those expand to the list of words in your script's parameters, not to each parameter as a separate word.

Instead of using a for loop, which will fail on spaces unless you redefine the IFS variable, I would recommend using a while loop combined with find.