Hooray! Glad this worked for you.
I had to do something similar 20+ years ago when I built my first complicated exe with PerlApp. How I figured that out is lost to antiquity.
If you have a somewhat recent version of PerlApp, I recommend using the GUI. This makes some of the options easier to understand. Just type "perlapp" with no command line args and the GUI will start. It is possible to add an icon for desktop display. I believe it is also possible to force arbitrary files into the exe although I would use that feature with extreme caution and I haven't done that myself. I can mention this now because you are solving your problem in what I consider "the right way". Forcing a .dll manually is not, in my experience "the right way".