When trying to replace a tool part with a vanilla wooden stick, a NullPointerException is trigerred.

It happen when calling newMat.ability(), into ReplacementLogic class, line 239.
I think this happen because when you try to get the ToolMatterial (ToolMaterial newMat = TConstructRegistry.getMaterial(newMaterialId); line 234), since it is a vanilla stick, it's not in you HashMap, so this is returning null.

Of course, this error does not happen with TiC tweaks's wooden sticks.

Right, SlimeKnights/TinkersConstruct@0b7a8f6 broke that. Fixed.