The All Purpose 4" ($12.00), Razor 4" ($27.00), or Tungsten Carbide 4" ($27.00) all work well - my favorite it probably the tungsten 4". I wouldn't over analyze it too much, they are all considerably better than you are currently using. If you can only afford one pair just cut wire deep in the throat and save the tips for fine work. I've given up trying to buy anything locally - just order them from the big "C".
Alot of fly tying scissors do have serrated edges, my Dr. Slick's do. It all depends on the model but, like hair cutting scissors, it's just for trapping material in the blades as they close instead of having it slip out, which is why some scissors with serrated edges are marketed as "hair scissors", for cutting deer hair, or any other various fly tying hair. Personally, after using a serrated pair of scissors, I'll never buy smooth bladed ones again.
I doubt that you can have the serrated scissors sharpened more than once if at all, without loosing the serration.
I use the Arrow and the All Purpose and a set of Anvil for heavy duty stuff. When I eventually wear out the serrated scissors I would like to try a set of the Carbide. Carbide is hard as heck with a crystalline like structure to the metal, that makes it very brittle.
If you are fairly new to tying you will probably nick them before you dull them.
Got the scissors in, love semi-local sellers. Gosh. The craftsmanship between these scissors and my cheapos is evident the first time you pick them up. Then when you start cutting. The feeling is similar to holding a point and shoot then holding an SLR. Or drinking a Budweiser then having a Boundary Bay Scotch..the list goes on. Tough spending the $25.00 on it but not regretting it now.
Non-serrated fly tying scissors can be sharpened by a professional scisor sharpener. There used to be a guy who hung a couple of evenings a week in the back booth at the Blue Moon in the U. District. He would sharpen any and all scissors. He did a good job on my fly tying scissors.
Check with your barber He/she may be able to direct you to a scissors sharpener -- if they aren't serrated.
I have anvil, Dr,. Slicks, and Tiemco. I really like the Tiemcos. I have had them sharpened, and they were good as new. The Dr. slicks do have micro serations(sp), whitch would be gone after one sharpening.
I went to the local fabric shop to find out who does their sharpening. I met the guy, and he said he could sharpen my sissors. I have had him sharpen all my knives and sissors ever since.