If I've got this right, you want to buy at EDI airside something that is not available at LHR. Then take it on the plane in carry on, before making your way home from LHR?

Or is the plan to buy landside in EDI and check the case in?

The mind boggles as to what may be purchased at EDI that is unavailable at LHR and worthy of the hassle involved.

I would suggest plenty of bubble wrap or towels in your case as a precaution against the bag being put in the hold.