What you need is the ShellExecute function from the Win32 API. ShellExecute reads a file's extension and starts the associated application that handles that file type, just as if someone had double clicked on the file in explorer.

#!/usr/bin/perl

use strict;
use warnings;
use Win32::API;

my $ShellExecute = new Win32::API("shell32", "ShellExecute", [qw(N P P
+ P P N)], 'N');
my $hWnd = 0;
my $filename = 'c:/public/test.pdf';

$ShellExecute->Call($hWnd, 'open', $filename, '', '', 1);
[download]

I didn't munge it into your example, but it should be pretty straightforward to do.