perhaps - untested -:

#!/usr/bin/perl

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

# I think this is the fastest way for the trim functionality...
# 2 statements benchmark faster than one statement

sub myTrim {
    my $str = shift;  #shift faster than @_ for one paramater
    $str =~ s/^\s*//; #no space at front
    $str =~ s/\s*$//; #no space at rear
    return $str;
}

my @fileTags = map{myTrim($_)}@fileTags.
@fileTags = uniq @fileTags;
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Update: I did run this:
Your Trim function does not trim the trailing spaces because the match (.*) is greedy...

#!/usr/bin/perl

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

sub myTrim {
    my ($str) = @_;
    my ($trimmed) = ($str =~ /\s*(.*)\s*/);
    return $trimmed;
}

my $x = "x    ";
$x = myTrim($x);

print "$x!\n"; #prints "x    !"
[download]

Update: The single statement version of your MyTrim() would be str =~ s/^\s*|\s*$//g; I saw one benchmark where that appeared to be faster than the "standard" 2 statements, but I was never able to re-create that result myself. Perl regex performance can vary significantly between releases - in general things get faster - but hiccups do happen.