Use of wooden bullets is really not a fantasy. In WWII the Italians actually used wooden bullets that were soaked in garlic! The thought was that if the person didn't die from the bullet wound, they definitely would die from the infection that the garlic would cause. The Mob also used this tactic on some of their hits. The Germans also used wooden bullets.
It's not like-for-like though . These were intended as training rounds or riot control . For Buffyverse vampires you need penetration and accuracy . Splinters are good and all but only if they travel . It's not as easy as just switching to a wood tipped cartridge with firearms . I'm sure it's doable with large caliber air weapons , with shotgun slugs , with muzzle loaders , with heavy machine guns ... but I don't think the average sidearm would work that well .
I'm not a gun anorak or anything

. I just did a bunch of idle fan research on wooden bullets ...and I was a bit unimpressed with them as a fantasy offensive vampire weapon

. I figured you'd be better off with a bolt thrower for offence ,holy water and a regular sidearm for defence . I figure the impact and damage of regular bullets is more of a deterrent than missed heart shots.
Thinking outside the box might be fruitful too . Captive bolt gun ? Nailgun ? Staking the heart is a very specific job : maybe specialized tools is the way to go ?
Something like the M134 minigun fires so relentlessly , any bullet performance loss is offset by a hail of other bullets .
This badboy already has a plastic bullet option. It could do a wood dart, a regular bullet , a holy water ampule , tracer , a silver slug ...all at the same time

. A few of these round the Hellmouth would keep demonic infestations to a bare minimum .
Another factor that occurs to me is just how 'wooden' does a projectile have to be to still have dusting capability ? If you can mess about with epoxy or liquid metal ,you could likely create a bullet with comparable ballistic properties to a regular one .