Wattle and Daub is not mined faster by any tool type.
In the renewed version of the mod only, you can also craft wattle and daub stacks, which are similar to the pillars available for brick-type blocks. These only have a connected texture in one direction unlike the regular wattle and daub block. They can be crafted as shown below.
In the real world, wattle and daub was traditionally made with wooden strips pasted over with a mixture of materials - wet earth, straw, and even animal dung! Though often associated with medieval Europe, the technique was developed by people in several regions, from prehistoric Eurasians and Africans to indigenous North and South Americans.