Hello Ann or Alex,
To get your strick meaning you would use the word
ergazomai .
Katergazomai means something different.
Now I can see where this will get sticky. You will rely on one source for explaining Greek and I will use another. I personally have no training in Greek, but the website I link you to is the one my Pastor uses and it supports the "show or demonstrate" meaning.
The other thing that supports that meaning is the context of Philipians and the overall message of salvation throughout the NT.
Example: When you read the parable of the sower you see that works result after accepting the seed (Word of God). If you accept the Word of God in your heart it will produce fruit (works). Therefore, works for God can only come after salvation, not works for God produce salvation.
Sincerely
I don’t need any external source; I know what these words mean. Ergazomai is the broad sense of work as in produce through energy. Kat- is a suffix that indicates outcome of a process, “to work out”. If I had a nickel for every pastor that lies about Greek of which he knows nothing in order to defend his theological fantasies, I’d be a very rich man.