hmm, wood should be fine. which wood you choose might be a matter of taste. i can think of many snares that would get the job done, but you'd have to like it (at least for the moment) i guess.
boris williams used a dry sounding wood (beech?) but he tuned it low and laid a fat note for recording, it worked for the cure material (rock). someone else might not feel the same though.
metal snares can suit both jazz and rock too, you probably might want to look at darker tones, copper, bronze, hand hammered ones.
if possible, keep listening and trying till u check out something you really like!
cheers