Is the ball joint actually showing wear or looseness? If not, I would rotate the tires front to rear and see if the wobble changes. Does not matter how many miles are on the tires for them be a possible cause of a wobble or shake.
If the ball joint is worn you just need to pick the replacement method you think you are comfortable with. Either way is perfectly acceptable IF the new ball joint fits tightly into the old control arm. If you try doing just the ball joint and it goes in too easy, you really should replace the control arm. Sometimes that motivates people to replace the whole arm so it can be a one and done repair.