I'm trying to get some 3D Vision fixes working for the latest version of Skyrim, but the fixes supposedly only work when using DirectX 9 only, and for some reason I'm Skyrim is using DirectX 10 for me. Is there a way to force Skyrim to only use DirectX 9?

Skyrim is a DX9 game, so it cant be using DX10.

then why is there a directx 10 folder in the Skyrim folder?

If you look inside the folder it contains an installer for DirectX which is the latest version & covers DX9/10/11, The folder name itself is misleading & leads you to think that it's a feature.
If only it used DX11....

Yup, sadly, Skyrim is DX9 only.

If a game is DX9, it is only DX9. You have to have 2 different executables in order to have DX10 and 9.

Because the Redistributable that contains the files is called DirectX10, well, now it is called DirectX11 for more current games. However, DirectX is backwards compatible and runs in DX9 mode for those games and DX10 mode for those games etc.

It's really simple. Just launch TESV.exe.