Can I replace a shattered glass screen without a digitizer replacement

I dropped my IPhone 6 on the top right corner onto concrete the other day getting it out of my pocket. The glass at that corner is gone and the screen has multiple cracks veining throughout the screen, but the entire screen is responsive which leads me to believe only the surface glass is damaged, not the actual touch screen. In fact, I'm asking this question with the phone and I am having no trouble. Is it possible for me to just get a replacement glass without paying $60-$70 on a new LCD/Digitizer/Glass combo? I just want to buy a $20 glass repair kit and simply replace the glass.