Two light-years is much too big. The two Pioneer spacecraft are expected to hit the heliopause sometime in the next decade and they are only moving at something like 25,000 miles per hour. If there really is an 'Oort cloud' out there, though, it will be 1 light-year or more distant.
So it really depends on how you want to define the 'limits' of the solar system. What practical use is the Oort cloud? What effect does it have in the game? (Assuming all stars have one...) Not much unless we allow it to be 'harvested' somehow or other.
Using the orbital domain of planets seems much more practical for the purpose of the game. If you use the orbit of Pluto as the 'limits' of the solar system you get a much smaller area. Pluto is anywhere from 4 to 6 'light-hours' from the sun (it has a highly eccentric orbit). Even with the larger distance light can cover the 'entire' width of the solar system in only 12 hours.
Assuming that our solar system is fairly average, SE IV ships only need to travel at about 1/60th of the speed of light (less than
2 percent!) to be able to cross the solar system in one month. 300,000 km/sec divided by 60 is about 5,000 km/sec or 3,100 miles per second. Still quit a clip. Out fastest spacecraft to date only do about 7 or 8 miles per second.