This really depends on the technology level the space empires have reached. The best way to move a giant gravity well is ultimately gravity.
As Samuel pointed out, the mass you list isn't large enough to become a black hole on it's own...but there's possibly methods of forcing a collapse at some tech level. Maybe?
The first to note is this really isn't a quick assault. Even if you are capable of accelerating a blackhole to the 10% the speed of light, the travel time between the closest of star systems is still in the 40-50 year travel range. So this attack is an extending of the conflict really...it's not going to be quick, the opposing empire is going to have years of time to attempt to respond and they'll likely see it coming. If they are both on the same tech level, odds are that if one side was capable of moving the black hole, the other will be capable of slowing it down or deflecting it. If the blackhole can get up to 50% the speed of light, it's still a 6-8 year travel time between extremely near stars. Empire A launches the blackhole, Empire A manages to overwhelm Empire B's system, and several years later Empire A's newly acquired territory is about to be destroyed by an attack they launched years ago themselves ;)
The best way I can see a black hole being moved is by a civilization capable of manipulating gravity and energy. Energy is used to create a mass near the black hole. The black hole begins moving towards this mass like a ball rolling downhill. When the two are close enough, the mass is disassembled into it's energy state and relocated a bit further away and moving in the direction the black hole has started to. This process is repeated (potentially adnasuem) and slowly the blackhole is accelerated.
Of course this is using our knowledge of physics. A potential alternative would be something similar to an Alcubierre drive where you are warping the structure of space around the blackhole...though in this case the blackhole isn't really moving quickly. Is that a potential that one of your empires has access to this?
If the Empire that launched the attack is capable of converting matter to energy...is there anything stopping the Empire being attacked from having the same technology to convert mass to energy and can simply convert the blackholes mass over to energy and basically use it as a giant energy battery?
As a conclusion...unless there is a fabulous future technology that these space empires possess that is far beyond what we know now, this really isn't a feasible attack. The time frames involved and the energies require just aren't that realistic and a race that is capable of moving it is just as likely capable of converting the mass of the blackhole into energy and using it as a power source. There are better things for these empires to invest their time and energy in...firing a stream of neutrons accelerated to 99.9999% the speed of light for example.