If you don't care about platform portability, you could try the Win32::GUI module instead of using TK, as well as the Win32::Clipboard module.

Here is some sample code to demonstrate how to do what you are looking for using Win32::GUI and Win32::Clipboard:

#!perl
use strict;
use warnings;

use Win32::Clipboard;
use Win32::GUI qw();

my $clipboard = Win32::Clipboard->new();

# Create an accelerator table to map keyboard shortcuts to subs
my $accel = Win32::GUI::AcceleratorTable->new(
    'Ctrl-C' => \&CopyListItems,
);
# Create the main window
my $window = Win32::GUI::Window->new(
    -name => 'mainwindow',
    -text => 'Win32::GUI Listview Sample',
    -size => [320, 240],
    -accel => $accel,   # Associate accelerator table with window
);
# Create a listview control with the main window as the parent
my $listview = $window->AddListView(
    -name => 'listview',
    -pos => [5, 5],
    -size => [$window->ScaleWidth() - 10, $window->ScaleHeight() - 10]
+,
    -fullrowselect => 1,
);
# Insert 2 columns
$listview->InsertColumn(
    -text => 'Column 1', 
    -width => $listview->ScaleWidth() / 2,
);
$listview->InsertColumn(
    -text => 'Column 2', 
    -width => $listview->ScaleWidth() / 2,
);
# Insert some data
$listview->InsertItem(-text => [1, 'a']);
$listview->InsertItem(-text => [2, 'b']);
$listview->InsertItem(-text => [3, 'c']);
$listview->InsertItem(-text => [4, 'd']);
$listview->InsertItem(-text => [5, 'e']);

# Show main window
$window->Show();

# This is our dialog loop
Win32::GUI::Dialog();

# This is the sub called when user presses Ctrl-C
sub CopyListItems {
    # Get a list of indices of selected items
    my @items = $listview->SelectedItems();
    # Will return an empty list if none selected, so we just return
    return unless @items;
    # Empty the clipboard
    $clipboard->Empty();
    my $text;
    # Loop though each item
    # The text copied to the clipboard has each selected row on a 
    #  new line, with each item seperated by a tab
    foreach(@items){
        my @text;
        my $item = $listview->Item($_);
        push @text, $item->Text();
        my $subitem = $item->SubItem(1);
        push @text, $subitem->Text();
        $text .= sprintf qq(%s\n), join qq(\t), @text;
    }
    # Set the clipboard
    $clipboard->Set($text);
    return;
}

__END__
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Update: Fixed links.