Although I know how to remove images from header area from theme config, but just to explore another way, I tried removing all the images from "/images/header/" folder. I got a few warnings which should be there for sure.

There are three fixes which need to be for this.
1) Put if condition before sorting images in random file generating file,
if ($files)
sort($files);

2) Put if condition before foreach loop in same file

3) Put if condition in the header config file, wrapping whole image container.

My webpage for your reference is, expertsguide.info.

4) leave a image in the folder - this will reduce teh code being executed and speed up processing (just a tiny bit, but every bit helps)