I would rather use a hacksaw to cut a flathead in. Set it up with a guide and know how many strokes you need.
Anyway what will probably be simpler is go find your local electronics repair/fiddler and they will have a pot of screws from dead devices. Most of them will be something more sociable in terms of head type and probably have enough of the right length or longer which you can happily cut down* if it is a blind hole or too ridiculously long.
If asked please do go pose with it for their girlfriend/wife/mother/... as vindication for keeping such things rather than throwing it out because it might be useful one day.
*the otherwise useless (seriously other than what I am about to cover they are useless) set of wire strippers that everybody seemingly has
The holes at the top there are for chopping down screws. That one courtesy of the numbers looks to be imperial threads (probably the more common in the US, see different ones around here but enough of my pondering tools) but if you have a metric one and it is the right size then if it also has threads that is for cleaning the thread up afterwards.
Pro tip there is do it in a bag so you can get the bits back and not have to go chasing a now even tinier screw across the room or sliding over the cut off bit later.
Though a decent hack saw will probably also do, as might a bench grinder or file if you have the means to hold it.
Beyond that I would love to be able to say M whatever or MF whatever but I struggle with photos when something is that size and don't have one here to measure.
Don't think I have seen replacement sets of screws either (sometimes you get those about this in a device lifetime, will probably cost a lot more than buying them individually from a fastener shop but hey) but have not properly gone looking. The same people selling replacement shells might not turn down a request either.