I experienced weird skyboxes to appear when applied conversion from Unity 4 to 5 in my asset. Weird thing is happening with clouds, where brightest areas are becoming black. Here is the result with Sunny1 Skybox:
Go to the skybox material, and it should show you each texture, and give you the option to “fix” it.
As for the skybox remaining, you can put a skybox on two ways - one with the component (that you removed). But the real way is in the lighting tab - you’ll need to remove it from there if you don’t want one.
if you just upgraded from unity 4, try going into the lighting window for each scene and it will ask you to upgrade to enlighten. This fixed funny skyboxes for me.