Given that he mentioned dropping $1000, I'm guessing he's talking about cartridge blades (e.g. Gilette Mach III), that cost a couple of bucks each and take up probably 20x as much space when packaged. Still not that much actual space needed. A small moving box would probably hold decades worth; definitely if stripped of the outer packaging.
That's 19 boxes of these, which probably fit in a shoe box.
https://www.amazon.co.uk/Derby-100-Extra-Shaving-Blades/dp/B...