The only type of knife that is suitable is a hook knife, but hook knives come in three varieties. The first is a hook shaped, curved blade and its cutting ability relies entirely on how sharp it is; even razor sharp it requires some tension in the lines to give it something to cut against, I would not recommend this as your primary, but could be considered if you wanted to carry two knives, as it is capable of cutting the webbing of a harness. Just be careful that you are not adding yet another place for a line to catch on when you attach it.
The second has a slot with a single blade in it, when tested it requires about 20Kg of pull to cut a kite line, sometimes more if the blade is not aligned correctly, but the force on the blade when it is used can damage it, making it far harder to use for a second line. These are the "bargain bucket knife" and are best avoided. If you have one of these in your harness you should replace it with the third type.
The third looks just like the second, but has two overlapping blades in the slot. They require less than a kilo of force to cut a line so do not bend in use and are the best choice of knife for our needs. They are very effective at cutting the flying lines that kitesurfers use.
Such double bladed hook knives are relatively cheap, a branded one is less than £20. They are slim enough to tuck into a harness when not in use. Because they can be tucked away they cannot accidentally snag a line. They often have a Velcro patch to help keep them in place, so they are exactly where you expect them to be when you need them most.