Not to worry
Shooting down a satellite looks not to be much more difficult than launching a satellite into a desired orbit. It's just a matter of launching into a desired orbit that intersects the target's orbit at the time the target passes by. It's less difficult than,for example, mooring with the ISS -- after all unlike the ISS situation, there's no need for the satellite killer to precisely match velocities with the target. Really, any nation capable of launching a satellite could probably shoot up a low orbiting satellite if they truly wished to. Per Google search, twelve countries whose have put satellites up on their own launch vehicles -- USSR, USA, France, Japan, China, UK, India, Russia, Ukraine, Israel, Iran and North Korea plus the European Space Alliance.
My guess is that the USSR, US, and China at least probably are already prepared to disable everything orbiting not belonging to themselves they think to be a militarily useful vehicle (photointelligence, communications intercept, launch detection, radio relay, probably geolocation) on a few hours notice.