I am using WWW::Mechanize::Firefox and cannot figure out how to click on the buttons once I get them using xpath.

You seem to be following the documentation, meaning you're doing it right

#this hangs

great, its FAQ :) https://metacpan.org/pod/distribution/WWW-Mechanize-Firefox/lib/WWW/Mechanize/Firefox/Troubleshooting.pod#Clicking-on-a-link-makes-the-Perl-script-wait-forever