First of all, the board in your NUC6i3SYH NUC is known as the NUC6i3SYB. Intel's naming convention uses 'H' for Hard Drive Chassis Kit, 'K' for Non-Hard Drive Chassis Kit and 'B' for the board itself.
The Technical Product Specification (TPS) for this board is available here: Intel NUC6i5SYB and NUC6i3SYB TPS.
You are correct; you require one (or two) 4-pin cables. I bought mine through Amazon USA (see here: Amazon.com: USB A Female to 1 X 4 Pin Internal USB Connector 1.25 mm Pitch). Unfortunately, I cannot see this product on Amazon's UK site, so likely you will need to contact the vendor, Micro SATA Cables, directly. My understanding is that StarTech.com UK carries Micro SATA Cables products, so you could try there as well...
Hope this helps,