Ok, I haven't received my new part yet (I think it might arrive tomorrow) but in anticipation of this I thought I set about taking the old one out.
I can confirm that you absolutely MUST, MUST...(did I say MUST?) remove the mirror housing to do this job!
There are actually two, CROSS-HEAD/PHILIPS type screws (i.e. different from the 6 Torx head ones that you already needed to remove to the casing) that hold the indicator lamp into the mirror casing.
If you make an attempt to remove the the lamp from the casing from the front by levering it etc out you will DEFINITELY SNAP your mirror casing and still won't have achieved the job necessary to replace the lamp!
You will also need to disconnect the two thin wires for the mirror glass heating in order to remove the glass. This was actually the hardest step for me as they were on really tight on my car and the the wires and spade connectors look quite fragile.
So,
1) Remove the glass (this simply levers off on UK cars but I have seen videos of U.S cars which seem to have an additional metal clip near the top of the mirror) and its two wires.
2) Remove 6 Torx screws: 3 are silver in colour holds the big black round part of the mechanism; 3 are black releases the outer mirror casing/cup.
3)Remove the outer casing away from the car and off after removing a small white electrical connector that's inserted near the upper part of black plastic of the mechanism.
4) Then you will clearly see 2 silver coloured, small Philips type screws. Removing these allows you to remove the indicator itself from the casing.
I can also confirm that the correct part number (as per the stamp on the plastic at the back) is : A 171 820 03 21