Space frigates aren't done yet Adwarf, wait a few turns
On another note the current U.S Minuteman III ICBM contains 1 W87 (500-600lbs) thermonuclear warhead, these warheads use a fission explosion (which is nescessarily self contained in the warhead to achieve correct pressures and therefore uneffected by space) to set off a secondary fusion reaction from which the explosive draws most of its power, a classic Teller-Ulam design, this design is perfectly capable of detonating in a vacuum without any major defects or troubles.
On the viability of space-flight for a nuclear weapon, there was a project launched by the U.S. airforce to accomplish this very thing. Project A119 was a U.S, initiative to launch and detonate an ICBM on the moon. The U.S was able to accomplish this in 1959, but the project was cancelled due to potential outcry from the public. While this project did not actually occur, it does demonstrate that we have had the ability to launch missiles at extra-terrestrial targets for atleast fifty years. And although the project was intended to be used with the much lighter W25 Warhead (200-250 lbs) it was also intended to reach the moon. Reaching geostationary orbit with a warhead twice that size is well within the realm of possibility assuming we're using current tech.
As for detonation the W87's re-entry vehicle is equiped with a targeting computer and self-guiding propulsion system enabling it almost pinpoint accuracy when fired at ground targets. As for a moving target, course trajectory can be altered via a ground base through missile operator staff using heavily encrypted and tight-beam radio transmission. This means before you could attempt to jam the radio signal, you'd have to first find the specific wavelength it's being transmitted on. So with that it's really a game of cat-and-mouse as ground control continually switches frequencies and you continually chase them.
In other words, yeah, i just want to blow up some space stations
why must you ruin my fun?