Found the citation. In the 1990s, B. Owen wrote a series of monographs under the general heading of WELSH MILITIA AND VOLUNTEER CORPS, 1757-1908. It has been years since I looked them but I believe there was one mongraph for almost all of the 13 regiments of Welsh Militia raised during the Great War with France, one for every county in the principality.
You might also look at Smith's NEW AND ENLARGED MILITARY DICTIONARY, 1805, as he is often useful for regs regarding officers' commissions, tc. I believe it is online.
WRT Ron's post below, Welsh militia units were stationed in Ireland during the war, while Irish militia units were frequently posted to England.