Jeremy E Crawford says here that (emphasis added by me):
The intent is that the druid uses the bonus in the beast's stat block for ANY proficiency the druid LACKS.
Meaning if the druid has the proficiency he can use it.
Weapon Master says I can choose four weapons to gain proficiency with.
If I choose claw, bite, sting and slam, would this allow me to add my proficiency bonus instead of the animal's to my attack rolls?
Are they weapons I can pick for the Weapon Master feat?