I don't play on a PvE Server, but I'm pretty sure there are no PvE quests in the FFA zone. The two quests for that area are PvP quests. So if you don't want to PvP, then don't do them. They are labeled PvP for a reason.
Funny...because walking an orb and tossing it into a power node that does literally nothing objetive / faction wise sounds a lot like PvE...killing droids in that area sounds PvE....the only thing "PvP" about it are the campers that have been griefing for days now.
If it was a "Kill X" or "take control of XYZ for a certain time to gain points," then it would be PvP.