I'm guessing you haven't been using artificial locomotion/direct movement in other games either, since thats a more general issue that you'll find with every game that uses it.
It definitely feels strange at first, but as long as you're not actually getting sick you do get used to it. Especially after several instances of exposure. Eventually it will feel completely normal.
I'd say the only thing that still gets me is moving with the trackpad, turning my actual body, and taking a step all at the same time - that will make me lose my balance a bit, but not like fall over or anything. I do try to avoid moving my feet while 'moving' in the game though.
The best tip I would give someone is to drastically reduce the movement speed (most games have a slider in the settings, incl. Skyrim). It feels a lot more normal when you are moving at the 'walk' speed instead of the normal speed. Then if you want to go faster, you can always 'sprint'.
If playing Skyrim isn't worth the experimentation required for you, then you should maybe also consider the modded version of Doom 3 BFG. It plays like a native VR game and is pretty awesome also, while being a more standard/accessible shooter experience.