A Welsh Assembly Government spokesman described the issues as disappointing because staff welfare was vital, while the director of the Royal College of Nursing in Wales said it was essential that any problem was reported.
As part of an assembly government initiative, Hywel Dda Health Board, successor to Carmarthenshire Local Health Board, and Betsi Cadwaladr University Health Board in north Wales are introducing the uniforms.
The assembly government said it was concerned because the welfare of staff was "paramount", despite the number of nurses who have reported skin irritation being "a minority".
A spokesman said: "As only a minority of staff have reported a problem, we have sufficient supplies of alternative uniforms for use. We are also working in partnership with RCN [Royal College of Nursing] and UNISON [union] to address any concerns as quickly as possible."
He added that news of the problem was "disappointing" as the fabric used in manufacture had undergone extensive quality control and testing.
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