Every single hex tile has its own Krita/Photoshop source file, where the elements are put one by one, with a mask on top which deletes everything outside the hex and then on top the border. So if you go into the source files, you could hide the border and/or the mask and create your own border and/or mask on top (which is, of course, some work you had to do for every single hex source file you need).
The image above shows the original hex (left), the hex without the border (center) and the hex without the border and without the mask (right).
For what do you need the hexes if I may ask (out of curiosity)? For Hex Kit, I wouldn't recommend thin borders or no borders at all.