Hi Dave,
I think you can find it with the find command (here an example for
the 'personal VM'):
[adm@dom0 ~]$ find -iname "*personal*"
./.config/menus/applications-merged/ and
./.local/share/qubes-appmenus/personal/apps/ seems to be good
candidates. Reading the Freedesktop menu spec could help you. Backup the
files before any (delete) actions.
Ludovic