Hello friend.
I included the following original HL2 bsp map files for the last release of OUTBREAK
d2_coast_01, 03, 04, 05, 07 & 09, as well as several others for the other chapters.
I just ran the stock installation for the last release & had no issues with the skyboxes in the Coast chapters. I am still using the GCF files from several months back so this could be due to the last big update that seems to mess a few things up, I have not been affected so far possibly cause none of my files updated or switched to the new format they apparently now use .
Perhaps removing the coast maps in your case may solve the skybox issue, but it might mess some other things up, or it probably will mess things up...as I had originally included them to resolve certain issues.
Wish I was more help to ya