The World of Ice and Fire sourcebook confirms that "Lord Reaper of Pyke" is just a self-styled title that the Greyjoys gave themselves, long before they ever ruled as exclusive kings of all the Iron Islands (long before the Andal Invasion). It doesn't signify sovereign status - i.e. even if a member of House Drumm was elected king by the Kingsmoot, the head of House Greyjoy at the time would still be called "Lord Reaper" of Pyke. There was some confusion about this for a while - but it doesn't make sense that the Drumms would call themselves "Lord Reaper of Pyke" when they ruled from Old Wyk, etc. The World book confirms that Aegon I Targaryen appointed the Greyjoys as the new "Lord Paramount" of the isles, they didn't have an alternate title.