Cat6 will be fine.
To nitpick, you drive them from dry contact outputs (relays) but on thr KLF200 they are not potential free, they supply 5V (iirc) on each channel. Note the terminals with black wires on the loom are all commoned together inside the KLF so you only need to connect one.
Making it look neat is another challenge, due to that horrific wiring loom. Probably best to hide the whole lot in another plastic box, but if you do give the user (or Loxone ms) someway to power cycle it as it does loose radio connection from time to time