I don't think you need to worry about cutting yourself on the case edges, BUT, I would still see this as an opportunity.
Unless I am missing something (entirely possible), the bracelet, dial, and movement are ~ worth the starting bid. Source a new case, sell the old one, and you have a nice vintage Speedy for a little over $1k.
You guys are better at this than me but this one seems pretty brutal, no? (back especially, 4 o'clock area) At a local used watch dealer for $1900 US...