Upon attempting to destroy a weaponsmith villager's job station to give it a new job, it would not search for a new job, even though I had not traded with that villager previously.  However, other villagers would take the weaponsmith's job when the station was replaced.  This resulted in about 4 weaponsmiths that I had not traded with previously along with 1 that I had traded with previously.  These villagers are sitting and staring at a single weaponsmith job station, and I have stopped picking up and replacing these stations for the fear that I will create more.  I have, however, destroyed and replaced other job stations and observed the expected result of: villager roams for a job and takes an open job station.

TO SUMMARIZE:

The weaponsmith will not search for a new job, regardless of whether previous trades had taken place, even if another villager has taken what was previously its job station or the station has been destroyed.