Well, I don't think there's a fourth sword, but if there is, I'd think i'd be Uriel's. It doesn't seem like raphael, michael or gabriel to have a hidden, secret, think; that's more uriel's style. If i had to connect him directly with any artifact, it'd be the lance, though. Why? Well, because uriel is the doer of bad but nessecary thing. He was the one who smote sodom, killed the first-born of egypt, ect. ect. He's the one who acts in secret, does things which seem bad, but for the greater good. Killing the Christ seems to fit into this mold. It's not nice, certainly, but it was merciful to end his pain and he needed to die as a sacrifice, a lamb of god. So if someone forced my hand, I'd say uriel was associated with the spear of destiny.
However, i think that's the wrong paradigm. While some arch-angels might have a greater responsibility than others, I think that all the swords are essentially under uriel's purview. Why? two reasons. First, there's the quote in ghost story where Uriel comments that when the other side circumvents free will, it is his job to step in with equal power to balance the scales. Secondly, there's the quote from Skin Game where he talks about something being expressed under "his purview," in the context of a change to the sword. This suggests to me that the job of uriel is to protect free will and the expression thereof, which lines him up with the overarching purpose of the swords, to free people of the influence of fallen Angels. That said, other archangels may be involved during specific expression's of the swords's power and faith - Gabriel might have been the one pronouncing judgement allmighty on the LoONs, for example - but i think Uriel is the overarching custodian of the swords.