"I really hoped that there is another callback which I haven't found."

The relevant code is App::Cmd::execute_command. As you can see, nothing happens between validate_args and execute that you could possibly hook onto.

One alternative approach could be to subclass App::Cmd, overriding that method with your own implementation that adds extra hooks between validate_args and execute:

{
  package My::App::Cmd;
  use base 'App::Cmd';
  sub execute_command {
    my ($self, $cmd, $opt, @args) = @_;
    local our $active_cmd = $cmd;
    $cmd->validate_args($opt, \@args);
    $cmd->before_execute($opt, \@args);
    $cmd->execute($opt, \@args);
  }
}
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Then use My::App::Cmd instead of App::Cmd.