There's nowhere to add a DoEvents() call because the offending section of code is only one line (my $response = $mech->get( $url );) that takes a couple seconds to finish.

Using a thread to allow your GETs to run asynchronously from your GUI is a good idea.

Using a queue to ship the data back to the gui thread for adding to the listbox is both unnecessary (you can add it from the same thread as you get it); and totally flawed if you use the blocking dequeue() call to fetch the data to be added, because that call blocks.

You could use dequeue_nb(), but that creates its own set of problems.

I'd love to learn more about Win32::GUI, if you're up to it

I long ago gave up on Win32::GUI because the lack of documentation made every minor code addition or change a nightmare of searching for examples, and trial and error.

As for what to use as an alternative, I mostly do without. But were I to have a need for a gui that could not be avoided, I probably plump for using HTML5 and the browser.