Sending file of custom python script with all parameters for popup interface already defined?

I think what you want to do is create a custom Toolbox tool and setup your parameters there. Then you would ship others your code along with the .tbx Toolbox file. See this section of the ArcGIS help.

Yes, as per @Chad Cooper's answer, you send the custom toolbox (*.tbx file) and the python script. There are instructions in the online help to do this.