I quickly perused the yardage books that I have for Irish links courses to identify courses with holes without a bunker. I found that either the courses had multiple holes without bunkers or all bunkers.
Those with bunkerless holes:
Royal Portrush Dunluce 4 holes (5,6,8,14)
Ballybunion old 4 holes (6,7,9,11)
Carne 7 holes (1,3,6,12,14,18)
Royal Portrush Valley 7 holes (1,4,7,8,9,10,13)
Doonbeg 2 holes (5,14)
Tralee 5 holes (2,8,12,13,15)
Those without bunkerless holes include Lahinch, Portmarnock, and Ballyliffin, Ballybunion Cashen.
It tough to imagine a better stretch of holes with minimal bunkering than 5,6,8 at Portrush and Ballybunion at 6,7,9