This is speculative, but too long for a comment.
One option you have for dealing with tools is that you can heat them hotter than food. You could try putting the cleaver in the oven for quite long periods, first fairly cool then hotter. Bare wood will generally darken but not char at typical oven temperatures, and I assume it's not vanished or otherwise coated as the flavour has soaked in (coatings may burn). Too hot and you risk losing the temper of the blade - if you know the exact steel you may be able to set an upper limit, otherwise you could stick to no more than about 120--150 C for caution.
You can also try soaking in alcohol as at least one of the relevant compounds is soluble in alcohol, and that won't damage the wood. I'd use flambé alcohol or surgical spirit/rubbing alcohol.
Wood treatments (such as linseed oil) don't generally soak in very far - so sanding the handle to remove the surface might work (possibly followed by refinishing). If the handle is riveted you might have to file down the rivets as well (sandpaper would be ok on brass rivets but not steel).
If the knife is so precious that you don't want to try any of these options, or if the wood gets damaged, you could see if you could get a new handle fitted.
In order, I'd go for heat first, then sand the surface bit not so much as to cause any rivets to stand out, then soak in alcohol.