Does a second One hit obliterator object actually exist?

It doesn't exist as an object you can pick up, but warping to Divine Beast vah Ruta and looking up for a whille allows you to see it when it falls.

There is no instances of the OHO beyond the one granted in the DLC, found in the Shrine of Resurrection.

That said, there are glitches that allow you to keep the OHO after the end of the trial.

Mini Game Storage: Keep the One Hit Obliterator

Effect: Lets you keep the One Hit Obliterator outside the quest it's meant to be used in

How To: Activate mini game storage with the Test of Wood escape glitch mentioned above, then start the Obliterator trial. You'll immediately fail the mini game due to having unequipped the Forest Dweller's Sword in favour of the One Hit Obliterator. Now, choose to restart the mini game. Monk Maz Koshia will say you've left the Great Plateau and that the trial has ended, but he won't take the Obliterator away. Instead, he'll take your current weapon, which is now the Forest Dweller's Sword. You'll then fail the Test of Wood again, and still have the One Hit Obliterator in your inventory, letting you use it whenever you want or hang it up in your house.

Notes: The One Hit Obliterator only does one damage outside of the Great Plateau, but will reduce Link to a quarter of a heart when used regardless. Dying with it equipped will not cause an instant game over either, and both Fairies and Mipha's Grace will now act as expected when using it.

Source

As for the Object Map, this is a tool built from data mining the game's code - outside of this tool, there is no records anywhere of a "second instance" of the OHO - likely making it a bug in the tool's code.

Without giving away any spoilers, the short answer is yes it does exist. Now for the spoilers...

The One-Hit Obliterator is more of a quest item than it is an obtainable weapon. Once you have downloaded the Champion's Ballad DLC, you should get a quest where Zelda basically tells you to return the Sheikah slate to the Shrine of Resurrection. Doing this gives you the OHO. However, upon taking it, the game locks you into a quest. 4 area's will now be highlighted in the Great Plateau, and you now have to go and beat all of the enemies at each location. Once you do, the OHO splits into 4 blue orbs which ultimately leads you to 4 areas near the divine beasts. There's then a bunch more to the Champion's Ballad story (and I HIGHLY recommend completing it), but the OHO can no longer be obtained; it will just be at the Shrine of Resurrection, although you can't take it anymore.

I would like to also say while the OHO sounds amazing, it limits you to only being able to take one hit before dying. Plus, it only can do 2 hits in a row before it needs to recharge for a bit. This honestly makes it pretty impractical when facing a ton of enemies, which you will once you get to that point in the quest.