A strike against Syria would be very unwise but would not, in the long or short run, significantly impact the global economy. A strike against Syria would likely do nothing productive (and would hurt American interests in the long run) but there would be no extended economic effect. The US is clearly not interested in a long term military strike, and Syria is not positioned geographically or economically to hurt overall world interests.
Because Syria is a small country with no exclusive exports, and not a major player in the current global economy, a strike against Syria would likely have little or no affect on the global economy as a whole. While there may be some localized economic issues, particularly in regions around Syria where current trade is highest, it is unlikely that small impact would cause any kind of larger economic issue on a global scale.