Can you steal something when someone isn’t looking in Skyrim

Unless you use the console there is no way to get the Skeleton Key back.

However, if you've got high enough lockpicking and have invested some perks that way, you could always grab the "Unbreakable" perk, which makes regular lockpicks work the same way as the skeleton key.'

When you use the console command to get the skeleton key the skeleton key breaks. The cheated skeleton key will respawn when broken but it's still not quite as good as the original skeleton key which can't be broken. When the cheated skeleton key breaks you have to find the place where the lock unlocks it. This can become annoying, but it does provide infinite lock picks.

I suggest not finishing the quest to return the skeleton key then you get the keep the original skeleton key. :)

So I tested @Mr Smooth's recommendation and it is indeed true.

If you have been caught, then you need to trigger a load* by doing a large zone transition. A small one (such as going from the ragged flagoon to the ratway) was not enough to cause the flag to be reset. However, transitioning from the cistern to Solitude was enough to cause the reset and I was able to immediately attempt to steal again.

In short, if you are in a town with a gate, then exit the town and go back in. Simply going into a house in the town is probably not enough to reset the flag. If you are not in a gated town, just fast travel to somewhere far enough that requires a load.