Depending on a size, probably on the order of tens of thousand.
Comets in the Oort cloud take very little energy to put on a collision orbit, the Sun barely holds them gravitationally, orbital speeds in the Oort cloud are measured in _meters_ per second. So they require (relatively) little energy to put them into a required orbit. It might be doable with just regular thermonuclear charges.
It will then take these comets more than a thousand years to "fall" from the Oort cloud.
