There were a great immigrant lads from many countries who found themselves slapped into a uniform as soon as they got off the boat. Because of the blockade, most of those immigrant boats landed at Union ports. I'm not too familiar with the experiences of Welshmen, in particular, but there were a number of units fighting under the "flag of green" on both sides, and many times they included numbers of men with names indicating they came for countries other than Ireland. Manpower needs were such that there was probably not much concern given to national origins.