The easiest way I know to convert a HDR (or nonhdr) skybox into a HDR cubemap1. Make a simple map that's just a hollow skybox, a light_environment, a player spawn, a small nodraw textured brush*, and a env_cubemap.
*Building cubemaps requires at least 1 face to be textured with a material that receives shadows. So texture some brush face with it, but that can't be seen by the cubemap or it will end up visible in the cubemap textures.
2. In the cubemap options, turn off SmartEdit and change the value to 10 if your skybox is 512x512 or 11 if your skybox is 1024x1024, and so on. Adding 1 doubles the resolution.
It is worth noting that the resolution for cubemaps is hard coded to be maximum 1024x1024 in some if not all source engine games though
3. Now choose your map's skybox, and compile with HDR.
4. Play the map and type "buildcubemaps" in console.
Keep in mind your screen resolution must fit a square that's at least 4x the cubemap resolution. So for a 1024x1024 cubemap, you should have at least a 4096x4096 screen resolution. Fortunately if you don't have such a ridiculous monitor, there's Dynamic Super Resolution. It's a graphics card driver feature that changes the screen resolution to a higher than the monitor's.
You can google it and figure out how to use it in 5 mins.
5. Now after you've built your cubemap (and restored your resolution to normal), use GCFScape to extract the hdr cubemap VTF file from the BSP. There should be several weirdly named VTF files, the one with the largest filezise should be it.
Drag'nDrop it outside and its ready to be used as a custom cubemap.