Do note that dipping Zen Archer Monk will get you a bonus archery feat and Wis to AC (which will be roughly equivalent to your light armor, effectively trading Flat-Footed AC for Touch AC). A reasonable DM will also probably allow you to use Perfect Strike with your gun (it's only 1/day after all). An insane DM will even allow Flurry of Blows with your gun, although I think most would agree that that's a little much.
Edit: You also lose 1 BAB but get +2 to all saves. I did it on my Gunslinger, mainly for the flavour of fighting unarmored, but I think it's a solid dip nonetheless. You can put the money you save on that +1 Mithril Chain Shirt towards better guns, or a +Dex or +Wis item.