It'd be easier if you just stored the list of keys in an array ref instead of a string

However, you could just parse the keys and traverse the data structure to find the proper value like so:

use strict;
use warnings;

my @array = (
    '{title}',
    '{Rule}{Severity}',
    '{Rule}{weight}',
    '{Rule}{id}',
    '{Rule}{version}',
    '{Rule}{title}',
    '{Rule}{detailedDescription}{VulnDiscussion}',
    '{Rule}{detailedDescription}{Responsibility}',
    '{Rule}{detailedDescription}{IAControls}',
    '{Rule}{check}{check-content}',
    '{Rule}{fixtext}{content}',
);

for my $firstKey (sort keys %hashData) {
    for my $arrayKey (@array) {
        my $val = $hashData{$firstKey};

        # Traverse to desired value
        $val = $val{$1} while $arrayKey =~ /\{(.*?)\}/g;

        print $val, "\n";
    }
}
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