Yes, you do have to remove the glass. There are two types of fitting, and unless I'm mistaken as you have a 16v yours will be the older type.
There is a howto but the photos have been corrupted and I'm not sure I follow one or two bits myself!
Push one side of the glass in (can't remember which) as far as you can, and in the enlarged space on the opposite side shine a torch to see the two ends of a large horseshoe-shape spring which holds the glass to the mirror.
If you can picture this, think "400m running track" shape that has 2 straight sides and two bends. One of these "bends" is broken and bent outwards - these are the two spring-ends you are looking for.
They lock in place, so your job is to lift+push the top one, and push+lower the bottom one from their respective clips.
You will need a narrow blade screwdriver to access them.
The glass should ease off - it's not held with a circular plastic grip like later models (unless someone has changed it like I have
* You cannot remove the black trim from the back of the mirror without removing everything
The likely trouble spot is the small screw that often corrodes into the rear aluminium casting. Lubricate well with penetrant to avoid shearing it or stripping the head.