To remove a wheel on a Shimano hub with a nutted cable, you need a wheel nut wrench, a thin allen key or section of spoke about 3" long. Needle-nosed pliers are useful but not essential.
Set the gear to slackest cable. The cassette arm has a small hole to fit a thin rod so you can relieve tension on the cable. Grab nut at end of cable, apply a little rotation and pop it out of the cassette arm bracket.
The wheel is now free to remove just using the wrench.
Reversing the process , you rotate the cassette arm using your thin rod, grab the nut, apply a little rotation and slot into its bracket. No further adjustment needed.