Be aware that chucking a pin vise and or smaller chuck into a bigger chuck adds rotational inertia (which helps snap smaller pits) as well as runout. Runout is not normally an issue with hand drilling although I have seen some Home Depot grade chucks that had enough runout you couldn't use them even in a hand drill, so it's worth remembering.
I would also caution that issues with chucks and cost cutting aren't just their size, but their holding as well. I *expletive deleted*ed up a lot of nice drill bits and driver bits by letting them spin in chucks that you couldn't possibly get tight enough due to crap design and assembly. For a screw gun that will mostly run hex driver bits, not a big deal, but for a drill and drill bits, especially small ones, it can make a big difference.
I've been slowly changing the chucks on my main drills out to vintage Jacobs Super Chucks (which are rebuildable) as I find deals on ebay. I confess, my cordless still wears the craptastic keyless it came with, but I no longer put round things in it.