I have this down now, without any damage to the figure or 'data-sticker'. All my mods now have the costume integrated into the base - Much neater.
It doesn't just have to be costumes though - You could also permanently power-up a particular figure with your favourite discs. You could have multiple 'duplicate' figures with a particular skill-set. Anyway -
* The easiest way to open the power disc is to lightly score around the red plastic circle first with a scalpel/craft knife.
* Then using 2 pairs of pliers, grip either side and just bend it down until the red circle and picture begin to lift. It's really important not to accidentally scratch or damage the sticker beneath, the tiniest mark will render it useless.
* The red circle/picture will not come off easily - BUT IT DOESN'T NEED TO! Force and great care are needed here. Only expose it enough to be able to 'un-peel' the sticker beneath.
* I use the craft knife again to grab the edge of the sticker, then carefully lift.
* The disc itself now is trashed and unrepairable - Bin it.
* Soften the figure's base in hot/warm water. Then use your pliers again to pull up the figures base from the disc beneath. Put something like a piece of cloth in your plier's jaws to prevent damage to the figure. Again brute force with care is needed here.
* Put the costume disc sticker in the circular base.
* At this point I place the figure on the INFINITY base to double check everything's working before I re-assemble.
* Super glue the Figure back onto the disc base. - There is a front and back, so compare the disc and base visually before applying glue.
* Push down snuggly and your done.