Here's how I would do it, with just a modification of your regex.

use strict;
use warnings;

my $input = <STDIN>;
chomp $input;

my $file = 'wordlist.txt';
open(INFO, $file);
my @lines = <INFO>;
close(INFO);

for my $word (@lines){
    if ($word =~ /^[$input]+$/){
        print "$word\n";
    }
}
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Udate: I may have misinterpreted the OP. This obviously will not work if all six input characters must be used.