Several of your opponents have Gunpowder (needed for Chemistry, which they want from you) and Astronomy, so enemy Frigates are a few turns away. If your neighbors are sufficiently weak/backward, you could pirate some crap out of them with a dozen guys, especially if the Frigate guys aren't interested in hunting far from home.
Your window is mostly closed, so don't bankrupt yourself, but you could throw a few guys out there for a little while, kick someone who's down, then pull back and hide in your cities until Combustion, snagging any careless ships that wander past. Getting more ambitious than that will wind up costing you in privateers, so you may as well not devote much energy to it, because most of it will be wasted.