I think it makes sense that there would be a council to decide who has the best claim. In the books it's made clear that such councils will tend to pick a man and will usually choose whoever they like best, regardless of which person technically has the best claim.
In that regard, it seems to me that if Jon is not an option, they would select somebody who at this point is relatively obscure or hasn't been seen on screen in a while, e.g. Edmure Tully, or Robin Arryn (w/ Yohn Royce as regent) or something like that.
Historically the southern lords were loathe to consider anybody from the north, anybody from the iron islands, or anybody from dorn.