If you are thinking of unsubscribing from sky then you will no longer need the dish nor Sky's box, nor associated connection cables.
I have never heard of a TV that shows both Freeview and Freesat. Here in the UK a few years ago we had Freeview or Freesat capable TVs that then needed either a Freeview or a Freesat box, connected to the TV. The Freeview or Freesat box then connected to the aerial which received both analog and digital frequencies which the box decoded as necessary.
Then came Freeview or Freesat capable TVs. No need for separate Freeview or Freesat boxes as one, (not both), was incorporated into the TV set. Around that stage all over the air frequencies had become digital and we no longer had analog channels.
As far as I know, here in the UK there are no TVs that have both Freeview and Freesat. So if you are getting rid of Sky you will need to buy either a Freeview or Freesat capable TV, or a Freeview or Freesat box to connect to any TV you already have.
HD channels bring another dimension to all this, as does so-called Smart TVs.
Mark