You don't have to farm Griswold at all since none of the TU's are absolutely necessary, but they are very useful. Each class has different results so using mules to transfer Gift Boxes over would be recommended but not necessary.
Usually doing Griswold Runs involve farming Tristram to kill Griswold for Gift Boxes which when transmuted in the cube produce 3 TU's usually designed for you class. It is recommended to mule Tiered Uniques (which are the ones you're finding) since they can be very useful for later when you trying to gear up your character and your hireling, as well as, saving them for other characters. If you are playing on Realm, you can use Sandbox or enable multiple launches of LOD through PlugY config in your D2SE folder to mule for other characters on Realm. Are you playing on realm or Single Player? If you are playing Single Player, then the easiest way to mule things would be to use PlugY or download D2SE Mod Manager and enable PlugY when you select whatever mod you wish to play.
