The redistributable in the DirectX SDK includes the whole history of the D3DX dlls. Installing the latest version of the DirectX redistributable should have your system end up with every version of these dlls. It is possible and allowed for applications to only install the files they need by deleting cab files out of the redistributable's directory structure, in order to reduce the size of the redistributable components, and this is how you can end up with having 43 of the dll but not 37 for instance.
If you remove the dependency of D3DX and D3DCOMPILER dll's from your application you can ensure the application will work as the d3d9 d3d10 and d3d11 core dlls are version-agnostic and are also tied to the windows service pack releases (i.e. D3D11 for Vista comes from Vista SP2 or Win7 stock installs for example).
Another possible way to remove the dependency and let the app startup is to make the dll a delay load module, so it is only loaded when needed (such as compiling shaders on a development environment). As long as you are sure the shaders exist on end-user machines properly it won't need to compile shaders and won't crash. Calling LoadLibrary and invoking the functions manually would be a safer choice with a way better error message of your choosing, but is a lot more work.