I would really question if a band-saw (a tool that —at varying scales— meat processors use to slice whole cows in half and lumber mills use to process whole trees) is really suitable for such a small and delicate job.
I'm not going as far as saying you shouldn't use a power-tool but there is another option that's a good compromise between the overkill of a powerful band saw and the slowness of the hand tools that others have suggested.
A band saw is going to be fast but come on... Even after safety, consider how many separate cuts you're going to have to make on these little guys.
Personally I'd opt for using a scroll saw with an omnidirectional spiral blade. If you're not familiar with them, they're essentially a blade that buzzes up and down in a fixed position and you move the wood around them.
That does mean the output will be less accurate than some other tooling but that's not always a bad thing, especially when you're dealing with little characters like this.
You can injure yourself on them but if you use the guard you're reasonably looking at losing a bit of fingernail instead of slipping and losing a hand.
The machines are very cheap but you'll probably get through a few blades.