Your link is not working right...but, anyway...
The safety will not fall out for a couple of reasons, but just taking out the lever will leave you with two sharp semi-circles of metal sticking out. To get rid of it, you will have to buy a whole new left-side only safety to replace it.
Or you could grind the end of the existing safety flush with the slide? Seems like I read about that years ago in a magazine article.