There are many things to consider here. If your triclinic cell is hexagonal, it probably just means someone was lazy to use P1 in the CIF file definition, instead of the proper space group. Then you can just convert the structure to hexagonal in the Builder, under Bulk tools>Lattice parameters (there you can also see if the angle is 120 and a=b). Make sure to keep fractional coordinates, and if the angle <> 90 degrees is not gamma, you will need to first permute the axes. In principle, if the Triclinic cell is equivalent to the Hexagonal (any crystal cell can always be represented as Triclinic) your calculation will yield the same result, but since ATK uses the cell symmetry to determine the high symmetry points, you will not be able to define e.g. the band structure calculation easily between the common points G,K,M, etc.
But perhaps your structure is not simple WS2 but some deformed structure, so check it carefully.