Be honest I wouldn't suggest it, my point above was to lap BOTH surface meaning heatsink and IHS, not remove it. I was just showing how small the core is underneath, so when applying thermal paste one can understand spreading it to the edges, isn't necessarily as critical, as the smoothness of the mating surfaces, and the type of thermal paste.
If your going to do it, I'd recommend this method below, and if you feel the center being umovable, it's silver solderd to the core, so leave it (that's nylon thread in the picture NOT wire, it's grey from the epoxy) You simply place the processor into the motherboard (to clamp it down) and "saw" away with the string. It takes time, but using any other object can expose the interconnect trace wires, just under the chip's surface. And especially at the edges;
