Note that after the dish is moved it will have to be re-aligned to make sure it is pointing at the Sky satelitte.
If it does not point to the satelitte you will not get any Sky signal.
So you could move it yourself, or get the Window people to move it, but you would still need to get the Sky people in to align the dish.
Also note the bolts that go into the wall are HUGE. If you dont fit it with the correct bolts it could blow off the wall and maybe crash into your new windows, and then you would have a bigger bill.
Get the Sky people in and get it done properly.