I'vee moved cories several times, and I've never been stung nor have they ever become entangled in the net. The trick is to place the netted fish in water so it can swim out.
i've only moved new cories from pet stores, and i just use a net that has pretty hard fabric to catch them and i just spin it around 360 degrees and they will go down themselves
I think I have had one Cory become stuck in a net with its pectoral spines, ever. I have moved many many hundreds of them, possibly thousands. I have kept Corys for almnost as long as I've kept fish, and I have worked with them as well.
I like to use a fine mesh net - coarser ones with larger holes could snag a spike.