Chosen Solution
I have some cracks and missing glass towards the bottom of my screen, and I would like to replace my battery. When I open the iPhone, will the screen fall apart if I melt the adhesive and use a sludge/pick around the edge rather than a suction cup?
I do plan on fixing the screen however iFixit has been out of stock for screens for a while. I usually have sticky tape over the cracks to prevent more glass from falling out of moisture entering the phone.
It is risky to take the broken screen off at this point. You can damage the LCD which would leave you with no picture, and like you said the glass is no longer stable so it can and probably will break more once you apply heat.