A no-sew conductive trace can be assembled by using Flat Flexible Connectors (FFC) and a conductive ribbon. Simple. Durable. Cost effective.
This conductive ribbon is from Fabrick in 100+ yard orders and has three conductive traces woven into the ribbon.
The FFC is available from DigiKey:
Male 609-2178-ND
Female 609-2160-ND
Please note that in this example the conductive ribbon has three traces and the cable connector has four crimping slots. When assembling your circuit align the conductive traces into the correct slots for both the male and female connector before clamping the connector.
VOILA! Simple no sew textile electronic circuits have never been so easy!