The play in the shaft will not cause wobble. Bad alignment, worn parts, improperly inflated tires, poor lift setup... Will cause wobble. The play may be the result of years of wobble or a few DW episodes but it doesn't cause the wobble.
If you put a body lift on it may bind.
Also check that the length is adjusted properly. Wrong length will place the joint at an angle that creates a dead spot in steering.
To remove the shaft there is one bolt under the dash near the firewall and one bolt under the hood where the upper and lower shafts come meet. Just push the splines of the upper shaft together. Then unsnap the rubber grommet from the firewall. From there, just pull the shaft out through the firewall.