I think trimming them down to a consistent width and overcasting them with a fine thread should be fine. I don't go as small a an eighth...wouldn't trust myself, but 3/16" I can manage. I think the consistency is key. I usually do a second row of stitching just inside where I want to trim. This gives me a line as a guide for the trimming, and it controls the gathers, which can be inclined to movement which otherwise causes your trimming to wander...or maybe just look like it did. I think I've also done a tiny Hong Kong type finish... just the tiniest bias strip to cover that raw edge, in lieu of overcasting. If your serger does a two thread stitch, I even think that would be okay, though I have that and would still be inclined to do a sewing machine overcast as my first choice.