Sometimes brute force is best. Here two foreach loops iterate the parameters of substr. The function uniq in the module List::Util removes the duplicates.

use strict;
use warnings;
use List::Util qw(uniq);

my $given_string = '0ae4bb830';

my @results;
foreach my $pos ( 0 .. 9 ) {
    foreach my $chr ( '0' .. '9', 'a' .. 'f' ) {
        my $out = $given_string;
        substr( $out, $pos, 0 ) = $chr;
        push @results, $out;
    }
}

{
    local $, = "\n";
    print uniq(@results);
}
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