The use of conductive stainless steel needs some more thinking through. It doesn't knot well, and needs some glue or nail polish to stay put. So see and behold, my prototype with alligator clips:

I also soldered the IR module. As I still plan to sew the whole thing together, I made hooks for the aligator clips (or wires) to grab on. It is not the nicest build, but it is functional.

I'm a bit concerned, the signal seems a bit weak for high power leds. But a test with an IR reciever and the default blink sketch gives a nice signal:

Received:
OFF ON
2196 usec, 180 usec
int IRsignal[] = {
// ON, OFF (in 10's of microseconds)
18, 0};
Received:
OFF ON
2236 usec, 120 usec
int IRsignal[] = {
// ON, OFF (in 10's of microseconds)
12, 0};
Received:
OFF ON
2236 usec, 140 usec
int IRsignal[] = {
// ON, OFF (in 10's of microseconds)
14, 0};