Application works fine in the Editor, but cant find an external DLL in a build

TL;DR: libvlc can't be loaded in a build because its dependencies can't be loaded. But Dependency Walker shows a tree with hundreds of DLLs in it, so I don't think I should just copy them all into the project.

I'm using HyperVLC, which is a C# wrapper for libvlc.dll, which is part of VLC media player.

The HyperVLC example includes the following function:

 [DllImport("kernel32.dll", SetLastError = true)]
 public static extern bool SetDllDirectory(string lpPathName);

In Awake, I call SetDllDirectory(@"C:\Program Files\VideoLAN\VLC"); which allows the Unity editor to find libvlc.dll without needing to put it in the project, but for some reason it doesn't work in a build (windows standalone), it just gives me "DllNotFoundException: libvlc".

I've also tried putting all the VLC DLLs in the project (next to Assets and in Assets/Plugins), but that doesn't work either.

Googling has led me to believe that the error actually means that the dependencies of libvlc.dll can't be loaded rather than the DLL itself. So I got Dependency Walker to take a look at it, which gave me the following tree:

 - LIBVLC.DLL
     - LIBVLCCORE.DLL
         - ADVAPI.DLL
             - About 20 more DLLs, some with more dependencies.
         - KERNEL32.DLL
             - NTDLL.DLL
         - MSVCRT.DLL
         - SHELL32.DLL
             - About 100 more DLLs, some with more dependencies.
         - USER32.DLL
             - About 10 more DLLs, some with more dependencies.
         - WINMM.DLL
             - About 10 more DLLs, some with more dependencies.
         - WS2_32.DLL
             - About 20 more DLLs, some with more dependencies.
     - KERNEL32.DLL
         - About 40 more DLLs.
     - MSVCRT.DLL
         - About 40 more DLLs.

Most of those sound like Windows DLLs, so I don't understand how the editor can find them perfectly fine while a build can't. And if this is actually the problem, I don't understand why the editor wouldn't just copy all the required DLLs into the build when it already knows where they are.

How can I fix this problem?