My V7 III Milano has brushed aluminium side covers.
I have ridden a V7 III Stone which has plastic side covers. I don't know if the Stone covers are the same as the Special's side covers.
I don't think the alloy side covers make much difference, if any, to the width of the bike.
When I first got the bike I kept bumping my feet into the foot rests when "paddling" the bike backwards into parking spots, but I got used to them and I don't notice them any more.