I would suggest using the Evil Status Icon Forever extension. Install it by clicking the On toggle switch HERE and open and edit the extension.js once installed:

gnomesu gedit ~/.local/share/gnome-shell/extensions/[email protected]/extension.js

You then change the section below by uncommenting what you'd like to hide, in your case "network" so it would look like so:

var removeStatusIcon = [

    // 'a11y',         // Accessibility

    // 'volume',

    // 'battery',

    // 'keyboard',

    // 'bluetooth',

     'network'

]

Ctrl+s to save.

The reason I don't suggest editing the internal panel JavaScript or modifying the network applets js itself either, is because upon updating either of these could be easily replaced and you would have to reapply your changes.