Blacksmithing specialization dilemmaFollow

The quest comments are vague and I couldn't find a straight answer for this right away, so I thought I'd ask:

My aim is to go into weaponsmithing > axesmith, but I also want the trinket from "Did you lose this"...

What I'd like to know is: Can I do the quests to get this trinket without binding myself to armorsmithing? In other words, can I switch to weaponsmithing after receiving this trinket or is it too late by then... To be honest, I don't even know if this questline is even related to armorsmithing but better safe than sorry, right?

I'll have to make this choice now, and since I don't want to forfeit my chances of becoming a weaponsmith or waste a lot of time/materials doing this questline for nothing.. I thought it'd be best to ask someone who's been there before.

I'm currently doing "The Old Ways", so I haven't picked up the quest yet.. As my sig suggests, I'm horde if that matters any.