We used to have a Victorian era house with one of these. We had to replace that wall in the bathroom and there was this huge pile of rusty razor blades in the wall. Had to use tongs to pick them up for disposal.
LOL, just use "cut proof" gloves. Nice to have around the house in any case. They're not fancy or expensive or armor plated, nothing crazy. I bust 'em out when a project goes away and I have to grab up a bunch of glass shards.
Cut proof gloves are a great touch. Are you using slices of bread? Dab the broken glass with the bread, ALL the shards will eventually stick in the bread, throw the bread away. Cleans it up quicker & better than a broom.