Regarding the 'clan' part of your posting. If your family were from Edinburgh/Fife, then they would not have been part of any clan. The clan structure was only a factor in the Highlands and Islands, and even there it had all but died out by the time period you are refering to.
As well as this, Dyer is an occupational surname. The reason you can't find many Dyer's in Scotland is the fact that the Scottish name for a dyer was 'litster', often corrupted to Lister. There was obviously dyer's/litsters required all over Scotland so (like all occupational surnames) the notion of them all living in one place within the same clan is nonsensical.
As has been written on this forum many times before though - for commercial reasons our tourist board and others are determined to fit every surname into a clan whether it's factual or not.