I doubt that Aragorn would have had any use for our (by now by serious and disparate overuse meaningless) term “cool”.
Anyway, as the stewardship had become hereditary like the kingship over a thousand years ago (surprisingly not that long before the stewards became Ruling Stewards in 2050 TA, though the Kings of Gondor had chosen their stewards from the descendants of Húrin of Emyn Arnen since about the middle of the 17th century of the Third Age – but that had been the personal choice of the respective king). So Boromir would have been (now non-ruling) steward, and I would rather expect that the plain “non-throne” that we find Denethor II sitting on when Gandalf and Pippin enter the throne room at the beginning of RoTK would have been removed. I would guess that Faramir, though not steward due to primogeniture, could very well have been a more influential advisor to Aragorn (at least in some areas) than Boromir. On the other hand, not all fighting had come to an end with the downfall of Barad-dûr until Aragorn could establish a “Pax Gondoria”, so Boromir’s undisputed prowess as a warrior and general would very likely have led to his being entrusted with not a few of these “mopping-up” operations.
As to Arwen … on her daddy’s side she shares a common heritage with Aragorn (64 generations down from Elros in terms of rulers of Númenor, then Elendil and Isildur and the kings, then chieftains of Arnor and Arthedain, as I once counted in my older paperback version of Robert Foster “Guide”). But on mommy’s side she is descended from grandma Galadriel (and don’t discount Celeborn’s ancestry too hastily), which brings in Telerin and more to the point Vanyarin royal houses. In one sense Arwen and Aragorn’s son Eldarion was the most noble human of all time, topping dad, in having the three royal houses of both the Edain and the Eldar as ancestors – often the actual kings. Need to widen that throne to accommodate both Aragorn and Arwen, or similar measures …
