I am coding a PyQt5 based GUI application needs to be able to create and run arbitrary Python scripts at runtime. If I convert this application to  a .exe, the main GUI Window will run properly. However, I do not know how I can run the short .py scripts that my application creates. Is it possible to runs these without a system wide Python installation?

I don't want ways to compile my python application to exe. This problem relates to generated .py scripts
No, to run a Python file you need an interpreter.
It is possible that your main application can contain a Python interpreter so that you don't need to depend on a system-wide Python installation.
Run generated .py files without python installation