Would that tighten up the shifter itself at the moment it has a lot of play in each gear, and when you say get a hurst shifter do you mean get the entire assembly I know that on the arm itself it says hurst.
No, only if it was not a Hurst. Usually replace the shims and get a new shifter sleeve, does the trick. I'd still make sure everything is torqued to spec. That can make a big difference. Not sure what a lot of play is... Side to side or 1st to 2nd or 3rd to 4th?