Spoiler'ed for great justice (see my post below) // Goober5000....
The GTI would have no way of exactly copying LuciferBeam technology. As far as we know in FS1 era, there was only one Lucifer, and it was the only ship with beams. When it was destroyed, it died in the node, and in Sol, and we all know what happened to the node. So really, the only thing the GTI have to go off of when building beam weapons is scans from Alpha One and other attacks by the Lucifer, and a whole lote of theorizing + guess and check. The GTI would use what they know, combine it with what they think works, and create a prototype beam cannon that would be the precursor to what we see now, as it would be the first Terran beam cannon. Thus, it being Terran, it should be green. It wouldn't be Shivan, because the GTI don't have the magical ability to just duplicate whatever technology they see. If they did, we'd see ships after Capella armed with BFReds....
You guy sforget that the Kayser used Shivan technology and design, but was not a direct shivan weapon in the sense that you wouldn't see it mounted on any shivan ships. It's reverse-engineered shivan technology, rebuilt and adapted to suit terran needs. Just as Beams are. The GTI took what they knew of the LuciferBeam cannons and made their own prototype. They didn't jack the beams off the Lucifers' broken corpse...
The exception however, are Shivan Turrets mounted on the Hades. However, these are explained through the GTA capturing the Taranis and checking it out, as well as the various cargo depots carptured. It's been theorized that the Shivans would have kept spare Beam Cannon parts in the cargo depots, but I highly doubt that. Namely because the Lucifer was unique, and invincible, as were the beam cannons.
In summary, it makes perfect sense for the Hades to have Green (if not a little on the weak side) Beam cannons, vs. t3h L\/CiF3R C4n|\|0nZ!!11