Computer fans are delicate. Delicate enough that they routinely break when people blow compressed air into them without holding the blades still. I'm 99% certain that putting a screw in the way of the fan's blades will permanently destroy it.
Your computer draws a pretty decent amount of power from your PSU, some of which is dissipated as heat. If you outright turn off most of the cooling for your PSU, it'll heat up like crazy and probably break. I don't know if modern power supplies have some kind of temperature failsafe, but I wouldn't bet on it.
just clean the damn thing outside