EOSS uses #30 AWG (0.25mm OD) Nichrome (NiCr) wire coiled snugly around about a 1 - 2 cm length of the nylon cord. I'm not sure which nylon resin it uses, but it's the stuff commonly used for woven nylon cord and rope. For 250 lb tensile cord, I use approx 7 - 9 cm of the wire, which yields an electrical resistance of 1.8 - 2.0 ohms; for 500 lb line, I use a shorter #30 wire yielding about 1.2 ohms.
The NiCr coil is silver-soldered to a a pair of 15-20 cm lengths of #16 AWG silicone insulated wires, and this cutter assembly along with at least 5 cm of the silicone wires are enclosed in a Styrofoam clamshell having 1.3 - 2 cm thick walls to prevent heat loss to the slipstream.
In both cases, current is delivered via 5A relay contacts and no more than 1 m of #16-2 cord from a series string of 2 or 3 LiSO2 N-cells (Li camera batteries). On command, the relay is closed for 10 sec, and cord separation, under tension, is effected within 4 sec typically. Cord tension us critically important to achieving separation; otherwise, the cord simply melts and sticks to the coil after the timed burn is complete.
This assembly is reusable. I have got up to ten good burns from one set of batteries. So long as the batteries will supply over 10A of short-circuit current (keep this test under 1 sec!), they are suitable for another flight. The NiCr coil lasts much longer - it should be replaced once its surface corrodes to the point that its resistance has risen more than 25% above the new value. After recovery, remove the coil from the clamshell and apply 3 - 5 A from an external power supply to burn off the remnants of the old cord. Then using a pointed mandrel, open up the coil just enough to allow the sealed and tapered end of new cord to be a passed thru using a needle; the coil should be snug, but just loose enough to allow the cord to be pulled thru to allow proper positioning of the burner.