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Ok. Managed, with a bit of a struggle and concern that the fastenings might break, to remove the fan/fins item, and then separate them. The fins had a little more dust on them but not so much as one would unduly worry about.
Of course, the now solid thermal gunge is now in two bits, some on the fin side, the other on the processor lid. Would need to go buy replacement (oh where is Maplin when you need them ?) but wondering what the best way to clean the old stuff off is, without scratching nor ruining the processor lid and the heatsink side. Any expert advice ?