Honestly, IMO something in your shell configuration is breaking things up. Try doing this to verify it:
zsh -f # starts a new shell ignoring your configuration
autoload compinit
compinit
./my-shell-script [TAB]
it completes with files. That is the default.
FWIW, if you want to bind a particular completer to a command/alias etc, you can do
compdef _jstack jstack
# simple _files completion
compdef _files my-local-python-script
# restrict to some file extensions
compdef '_files -g "*.(eps|ps|pdf)"' okular