You need a combination of three mods to make this work.
1. What the Hack?! to enable you to control mechanoids in the first place.
2. Mechanoids Drop Guns! (Continued) Makes your mechanoids (all mechanoids!) able to drop their weapons.
3. Character Editor Allows you to make your mechanoid drop its current weapon and pick up a new one.

First, select the mechanoid whose weapon you want to change, and open Character Editor.


Select the Inventory tab, then hold Alt and left-click on the 'drop' arrow, then exit Character Editor. This step will only work if the mechanoid can be manually controlled (can be drafted).


Upon exiting the Character Editor the mechanoid should drop its current gun.


Select the mechanoid once more and re-open Character Editor. Click the Inventory tab and click the Equipment button at the bottom. Select whatever weapon you want the mechanoid to equip.


The mechanoid should now have the selected weapon equipped. Exit Character Editor.


Enjoy your mechanoid's new toy!

All credit for this guide is due to Daijin. He created it on Imgur[imgur.com]. I just converted it to a Steam Guide so the infoirmation wouldn't be lost.