Custom texture wrap modes?

In the shader I'm working on, the texture doesn't cover the entire mesh. So I want anything sampled outside of a texture to return a set color (in this case just black). In the inspector, none of the default options (Clamp, mirror, etc) let me do this. Is there any way to make a custom wrap mode, or do I just need to check the bounds manually in the shader?

 

Unfortunately Unity does not expose the border wrap mode (which does exist). The options are doing it in the shader, or putting a single pixel wide black border on your texture, selecting Border Mip Maps in the texture import settings, and Clamp wrap mode.