Whatever you end up using, buy the best quality you can.
a cheap hole saw off of eBay or from down the market will most likely not be sharp enough to cut it without damage.
I like the idea of clamping wood either side but it might be tricky to mark out where to drill.
I'm not convinced that taking it slow would be the best approach, most hole saws have a standard drill bit type tip in the middle so you could go through with that then spin the drill up fast with it located and then go but i haven't tried that so don't go on my advice, it just seems that going slow would more likely chew it up.
Could you not get access to a pillar drill?