Rendering a Skybox with Post Processing

I want to render a skybox texture with some blur effects applied to certain objects in the background.

I followed this tutorial (https://www.katsbits.com/tutorials/blender/render-skybox.php) on skybox rendering, and am happy with how the blur appears in a camera render, but currently the post-processing is not applied when rendering an environment map. What’s the best way to solve this?

Thanks!