"used wood IN the bullets..."
Ok, that is just ever so slightly more viable, but I've never heard of it.
Other nations used various other materials in their bullets over the years in combination with more traditional materials.
Normally it was purely for ballistic advantage.
For example, Italian 7.35 mm bullets had an aluminum filler in the nose to lighten it.
Some Marks of British .303 ammo had a fiber filler in the nose.
In both cases, the idea was to make the nose even lighter, which in turn would make the bullet even LESS stable upon hitting the target.
Now, Huon DOES mention a variation in bullet construction for the 7.92x57 bullets...
"A lack of strategic materials led to the introduction, in 1930, of a ball cartridge with an iron-cored projectile, called "S.m.E," but commonly called semi-armor-piercing."
Huon goes on to mention the other obvious bullet variants -- steel and tungsten carbide inserts for armor piercing capabilities, and various types of chemical compounds, but absolutely NO mention of any bullets being either completely or partially cored with wood.
Given that Germany had VAST supplies of mild iron and steel at the end of the war, and was making bullet jackets and cartridge cases out of these materials, I don't see very much liklihood of them having used wood cores when they could have cored the bullets with iron a la the S.m.E projectile.