If the screw is rusted you likely have bigger problems as it really should not do that and I would wonder where it was dunked or kept that caused such a thing (anything like that also being in the cartridge itself and possible causing trouble).
I could unscrew mine and bust out the... would have to be micrometer. However what is likely a better choice is find whatever electronics nerd is around you that keeps a pot of screws and things from dead computers and devices, that or consult your own scrap pile (dead laptop DVD drives and hard drives is probably where I would start there). Possible alternative. It is about the size I see in glasses so maybe a trip to an optician or someone that otherwise fixes them as most of those will have kits to replace basically anything. If it is too long then no worries as you can probably cut one down with just about anything (pro tip do it in a plastic bag so when cuts rather than it pings off into the next universe it gets caught instead).