I have only been in one Wooden Skeleton Key room, but I have been there twice. The key was collected in another battle unrelated to the Wooden Skeleton Key room battle. I have since collect other Wooden Skeleton keys and have been told by others that they have other keys, IE. Stone and gold. I personally know of only two rooms that use the Wooden Skeleton Key, and have not yet found any other kind. I have not had nor been told of a Skeleton Room battle where a key was dropped. Not saying it can't happen. best of luck
Some of the dungeons where the locked rooms are found have possible drops of skeleton keys - wooden or stone keys keys with skulls on them. If you go in the Himoolayan dungeon, Zigzag Dungeons, and Barkingham Palace you can run the regular quests for the unlocked areas. During those fights, there is a chance you might get a key. If so, you can use it to let your team into the locked room, or save it for another time. I know there is at least one locked room I saw in a regular quest area, not a dungeon, in Avalon's crystal caves. If you hadn't run those dungeons I mentioned, and obtained a key there, I can see why you were wondering about it.
Jade Oni drops Wooden Keys quite often as well as the Ultra dungeons that drop keys as well. The regular bosses in Barkingham Palace drop Wooden Keys and in Lower Zigzag Stone Keys. The Ultra dungeons for Meowiarty, Rattlebones and Krokopatra drop Gold Keys.