I just want to report success with changing the shim and thank the OP and others.
I had no difficulty in accessing the nut on a Type S (FN) on the clutch, but I did have the car raised with the wheel, axle, wishbones off for replacement anyway.
The ring spanner went on easily out of my Halfords socket set, although it was difficult to turn due to corrosion. A bit of Plusgas helped. I did also manage to get a socket set in there, although it was a very tight fit. It didn't really offer me anything over the spanner though. I could have moved the water bottle out of the way easily enough if I'd needed to.
My clutch plate was corroded as you'd expect, so I took a hard wire brush to it, and then a much smaller, softer brass brush. You can get sets of 3/4 of these brushes for £3-4 from Ebay or Amazon. The plate came up much cleaner.
I then used the brass one on the compressor where the clutch plate would make contact, gently. It'll already be pretty dirty, but this will take off any corrosion on there. Finally, I wiped it all down with alcoholic wipes. You'll need a few, but it's worth it. The plate and the compressor will make much better contact.
I didn't use the same shims as the op suggested as I found sourcing them to be a bit of a pain. I did manage to find Interior: 10mm, Exterior: 16mm quite easily on Ebay though. The 16mm OD works well - in fact, I'd say better. I swapped the original and the 10id/16od a few times, and the slightly thicker one had less 'wobble' on it. The OD didn't seem to impact anything on the compressor, and the clutch engages instantly when it should.
If I was to do it again, I would go with the 16mm OD for sure. I used 0.1 thickness * 2, which meant the measuring gauge was within spec.
Cheers