Te Queen of Sheba's sword quest unfinishable?

I know that pickman has one fragment but the problem is that i completed the quest for giving him a job before getting this sword quest. So i never made any kind of a dealw ith him for any sword fragment (i avoided the whats in it for me option, because i didnt want to be taking money from beggers). Now when ever i talk to pickman he just complains about the work i gave him (what an ass), and has no options relating to the sword shard. I also tried knocking him out and taking it from his body but he doesnt have it on him.

So am i screwed and just simply unable to ever complete this quest? If this is the case then i woukd say this is a badly thought out quest. It makws no sense that i could at least off to pay him for the shard. It also makes no sense that he doesnt have it on him if he is supposed to gove it to you, he doesnt exactly have a house to store it in.