Would this entire wall need re-skimming or just where the wardrobe has been removed?
...can you skim up to the edge of the existing skim on the wall and get a nice smooth finish?


YES- an experienced plasterer, decorator, or painter could make it look nice by repairing just that area.


  ...would it save me money to fill in the holes...?


MAYBE- if you do it correctly you might be able to save the professional some time and materials cost; conversely, if you do it incorrectly he/she might have to tear it out and redo it correctly.

My feeling is that if you were skilled/experienced enough to correctly patch those holes (especially the large area of damage near the floor) then you would be capable of doing the whole job yourself. Since that doesn't seem to be your intent, I think you should let the pro do it all. The additional time and materials needed to repair the holes won't make a huge difference in the total cost of the job.