Who decide which check to make on a recall knowledge action?

In Pathfinder 2, a character can attempt a Recall Knowledge check to get some information about a monster. There are several skills that can be used for such checks, but only some of them work for any monster.

Let’s assume a player decides to use Recall Knowledge on an animated armor (as a Construct it can be identified with either Arcana or Crafting). How does it work? Here are two guesses:

  • The player chooses one skill she wants to use (either Arcana, Crafting, or maybe Religion if she thinks it might be an armor possessed by a ghost). The player rolls and the DM tells her about what she learns regarding that specific skill (for example if the player chose the skill Nature and rolled well the DM would say “this is definitely not an animal, a plant, a fey, or some other natural thing”)
  • The DM tells the player about which skill to roll (depending on what the monster is and which skills the character is trained in). The player rolls this skill and eventually get more information.

The first hypothesis seems more natural to me as a DM but my players told me it wasn’t supposed to work like that. Who is right?