the lord of the rings - What did Aragorn do with his sword between the battles of Pelennor Fields and Morannon?

After the Battle of the Pelennor Fields, Aragorn draws his sword Andúril and says:

"You shall not be sheathed again until the last battle is fought."

The Lord of the Rings, The Return of the King, Book V, Chapter 9: "The Last Debate"

The date is March 15; the "last battle" he has in mind is presumably the Battle of the Black Gate, which takes place ten days later, on March 25.

What did Aragorn do with Andúril for 10 days? He spent the first two days in his camp outside the gates of Minas Tirith, and the next seven days riding from Minas Tirith to the Black Gate.

We know from his dialogue outside Theoden's hall in Edoras that he is reluctant at best to lay the sword down, even in its sheath and under guard.

"It is not my will to put aside my sword, or to deliver Andúril to the hand of any other man".
-The Lord of the Rings, The Two Towers, Book III, Chapter 6: "The King of the Golden Hall"

He is eventually persuaded by Gandalf to comply with the guard's request to disarm, but only after delivering this warning:

"Here I set it, but I command you not to touch it, nor to permit any other to lay hand upon it. In this elvish sheath dwells the Blade that was Broken and has been made again. Telchar first wrought it in the deeps of time. Death shall come to any man that draws Elendil's sword save Elendil's heir."
-The Lord of the Rings, The Two Towers, Book III, Chapter 6: "The King of the Golden Hall"

In light of this, I can't imagine him leaving it unprotected in his tent. Did he walk around carrying an unsheathed sword for two days, then ride along carrying an unsheathed sword for a week? This seems like it would be dangerous, inconvenient, and fatiguing.

So how did he deal with an unsheathed, presumably razor sharp sword for a week and a half?

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Note: here's why carrying an unsheathed sword around is a bad idea:

Aragorn stood before the Black Gate, fire in his eyes, Andúril held firmly in hand, shining forth from his hip. Pippin, alight with excitement, ran to his side, and cried, "Strider! Whither has the Dark Lo----". His voice suddenly ceased, for Aragorn, turning to face the halfling, smote his neck with an unintended blow; grimly he gazed upon the ruins of Pippin's throat, and with displeasure saw the hobbit's head tumble down the slag pile, spilling from its helm as it came to rest in the scree below.

A tear in his eye, Gandalf spoke: "Ever and anon, even the greatest of men may chance to visit such misfortune upon one whom he loves". Aragorn stood silent, watching until Pippin's headless body, which had remained upright through some unseen force of will, began at length to waver, and finally, fell in a heap at Aragorn's feet. At last he turned away, fixing his eyes upon the fair face of his fallen companion, saying "Alas, I did not wish this thing, Peregrin Took, Ernil i Pheriannath, Guardian of the Citadel, son of Paladin of the Shire. Truly, I tell thee, though I fear it be of no comfort now - My bad, dog".

Answer

He was speaking figuratively.

Obviously he didn't plan to keep his sword actually unsheathed, for reasons of safety on several different levels, for the many days it would obviously take until he reached the last battle.

I've wondered about this exact same thing (hey, I'm a pedant too!) and satisfied myself with the following version, which captures the spirit of Aragorn's words but could be intended literally:

"You shall not be sheathed again permanently, with no intention to unsheathe you afterwards, until the last battle is fought."
_{-- The Pedant of the Rings, The Return of the Pedant, Book V, Chapter 9: "The Last Pedant"}

Edit: as Royal Canadian Bandit points out, the sword can be sheathed permanently if and only if there are no more battles, i.e. the last battle has been fought. So an even more rigorous phrasing would be:

"You shall not be sheathed again permanently, with no intention to unsheathe you in the foreseeable future, until the last battle of this ongoing war is fought."
_{-- The Pedant of the Pedants, The Pedant of the Pedant, Book V, Chapter 9: "The Pedant Pedant"}

Edit: as Wad Cheber points out, there were later battles in the War of the Ring in which Aragorn did not fight (e.g. the Scouring of the Shire). So an even more more rigorous phrasing would be:

"You shall not be sheathed again permanently, with no intention to unsheathe you in the foreseeable future, until the last battle in which I shall participate in this ongoing war is fought."
_{-- The Pedant of the Pedants, The Pedant of the Pedant, Pedant V, Pedant 9: "The Pedant Pedant"}