I am sorry to say that there are no fly fishing guides in Skagway. It is really kind of a black hole for fly fishing. The town is located in a very narrow and steep canyon that doesn't lend itself to much fishing. The main river in town is very silty and glacial.
If you have the time and inclination you could take a quick flight over to Haines and Greg Schlachter of the Expedition Broker can guide you. Otherwise, look for fly fishing guides in Juneau and Ketchikan.