I've read that monks avoid indexing into an array.

I think that's a mis-perception. Monks avoid iterating over array indexes simply to index it later on. So instead of

for (my $i = 0; $i < @array; $i++) {
   use $array[$i] here
}
[download]

They write

for my $a (@array) {
   use $a directly here
}
[download]

But there is absolutely no reason to avoid array indexing in general.

Should I be concerned about declaring my variables inside a while loop?

No.