I think other people have tried wrapping the mirrors but end up having to cut too many shapes for it to be an easy or long-lasting job. However the coloured mirror shells can be removed in situ and swapped for replacements e.g. in solid black. You just have to remove the mirror glass first. Adjust it fully inwards and get fingers or a trim tool in behind it in the corner and pop it off its mountings. Then there are three screws holding the shell on to the frame. Be very careful if your mirrors are heated (and in this case there are two electrical connectors to the elements on the back of the glass to remove) as they are not the cheapest to replace.
If you do want to get the whole unit out, first you have to take the door card off. The Search function will find a how-to for you. Disconnect the mirror wiring from the window control unit and remove it from its routing cable-ties. Then prise off the inner triangular cover in the corner of the window, there are another one or two screws underneath that hold the mirror unit on. The wiring and connector will fit through the hole it leaves, but there will be some dried-up putty to remove first. On refitting, put some form of stopping compound in to avoid leaks.