The exact way to do it depends on the style of press stud... my Super Tool has one of those "ring" type fasteners, that doesn't have a centre post, but more like a tube. And even after removing the fastener, it would not be easy to fit a new one without some kind of mandrel or anvil. Maybe some padding and then a steel bar inside the pouch, but the riveted construction makes it look as if it would not be straighforward.
For the "male" side, it's easy.
If it is a kind of mushroom shaped centre post, you can drill it out quite easily. Put a mark in the top of the post with a centre punch or a nail, then drill it out carefully with about a 3mm (1/8") metal cutting bit.
For the ring type, about a 6.5mm (around 1/4") bit should do it.
For the "female" side, just look carefully at what you need to drill out and do it slowly.