Can I replace home dye shampoo with my own?

One for the hair dye experts. I have a fragrance/perfume allergy but I want to add some blonde highlights to my hair. I bought the Jerome Russell Bblonde Highlighting Kit kit online and it seems the only element with perfume in is the shampoo that comes with the kit. I don't understand anything about the ingredients – will the kit work if I replace the shampoo with my own fragrance-free shampoo?