Tl;dr: I think it would be awesome to see Jon with a West Coast Customs’ style Pimp My Valyrian Steel Sword, made up of a Stark hilt made for him by Joer Mormont, Valyrian steel from the Stark ancestral sword Ice, and a sword that had represented the downfall of House Stark. It would be white and red, both hilt and sword, like Ghost and Weirwoods. Also, giving Dark Sister to Arya and Longclaw to Jorah feels right. In view of this, this is why there is no way it happens.

Oathkeeper to me is a lame name for a sword, not to mention, it represents the downfall of House Stark. If anything, this sword should be melted down and have its hilt thrown into the sea. Conversely, I would love for Jon to somehow get a hold of Bloodraven’s Dark Sister; maybe Bran could be the catalyst that brings Jon in contact with the sword. Then, Jon would be in possession of Longclaw, Dark Sister and a generous portion of Valyrian Steel.

I think it would be cool if Jorah somehow ended up on The Wall and was instantly a respectable figure there. Jon Snow, having heard of Jorah’s addition, would then be in a position to pass Longclaw on to Jorah, but preserve the hilt that Joer made for him. This would keep the sentimentality from it being a gift to Jon, and would allow Jorah to inherit what had previously been meant for him.

Next, Jon comes into contact with Arya and gives her Dark Sister. How this happens I would have no idea, but it sounds like Arya was destined to have a sword with this name, given to her by the same brother who made her Needle. Not to mention, she is going to want to have more than a sword made for stabbing.

So Jon is left with a sword without a hilt, which just so happens to be a large portion of the Stark ancestral great sword, “Ice”. So what does that leave Jon? A Valyrian steel sword that he can put the hilt Papa Mormont made for him on, which happens to look like Ghost aka a Weirwood motif. I think Oathkeeper also has bright red speckles, but I am not sure. If so, that would match well.