Have you tried A2? It hardens more after heat treatment but I believe it to be slightly softer without treatment. It should still have the integrity for a lanyard loop.
I found a source for metric, but I have never used them so cannot vouch.
http://www.flat-stock.com/~store/Mer...ode=PM-A2DRMM3
I get materials from 'inventables' but did not see that they have a2 in metric.
https://www.inventables.com/technolo...-drill-rod-a-2
If you are interested the closest to 3mm are:
7/64 = 2.7781mm
1/8 = 3.1750mm