Stepping from on camera flash to off camera flash can dramatically improve your results and modern wireless triggers are the way to go. Sync cords get old fast and have the obvious drawbacks unless you are in the studio and working in controlled conditions and even there, I've used wireless for years.
The obvious choice for a Godox flash is the line of Godox triggers. For your application I would suggest the Godox X2T-C (Canon) trigger since it also has a hot shoe should you pick up a second cheap flash to mount on your camera you still have control of the off camera Godox flash.
FWIW, I too have Pocket Wizards, Plus II's and Mini TT1 and Flex TT5. I also use legacy studio strobes and this is where the PW's still come in handy. However, I also have Godox AD Pro strobes and mixing the two strobes can be implemented by mounting the Godox X2T trigger on the cameras hot shoe and then mounting a PW in the triggers shoe thus allowing flash sync of 2020 strobe technology with er...um... my 1980'2 Speedotrons, LOL.