During the War of the Last Alliance — or basically as soon as Sauron's spirit limbed back to Middle-earth after his body got lost alongside Númenor and he got the One back from its hiding place where he had wisely put it before he surrendered to Ar-Pharazôn — what the Elves feared to happen at the end of the Third Age is already a given: Sauron has the One and therefore the Three are revealed to him if they would be worn, which is the reason they probably aren't worn?
Or do the Wearers think: He knows our plans anyway; a huge host (Elrond compares it to the Hosts of Beleriand at the Council) is on its way to Mordor, if our thoughts are revealed to him all he would perceive is that we come to take him down, rather obvious - therefore we can wear them, or would they already be tainted by that?
Granted, the Last Alliance is strong and manages to defeat him, and then Isildur loots the One from his corpse, but before that the Elves couldn't have used or even worn their rings, could they?
Galadrial has it the easiest: she can just take Nenya off and keep it hidden somewhere in Lórien. She doesn't fight and therefore can keep the hiding place a secret and guarded.
Círdan can sort of do the same and leave his at the Havens, but since we are told that only the Wearers know who each other are he doesn't tell anyone (as a failsafe if he were to fall in battle) - otherwise there would be one more person who knew that Círdan had Narya. There is a sort of loophole possible in that maybe that trusted person did not know that Círdan gave it away a millennium later, so that the "only the Wearers know" phrase would be correct again at the time of the War of the Ring.
What about Vilya, though? Did Gil-galad take his trusted herald Elrond aside and say:
"Hey if I don't make it through this thing, I hid the most powerful of the Three at place X. So if I take the express route to the Halls of Mandos, but we still win, it's yours. No idea what happens if you don't make it out either though. You think we should tell someone else…"
Maybe Gil-galad, prophetic as he is, knew Elrond would survive and it was deposited at Rivendell?
Or maybe they did the sensible thing and deposited all Three in the safest place - with Galadriel, the mightiest not partaking in the fight, in Lórien - and then she distributed them back out after Sauron's defeat and the loss of the One after the Gladden Fields? But can the rings be moved while Sauron possesses the One? Or is the act of carrying without wearing enough to reveal them?
Clearly, all I have is speculation so here is the question: Is it known where the Three Elven Rings were during the War of the Last Alliance?