I want to be able to sew 1mm cotton cord?

That's fairly thick, and will make a large hole in the fabric. The usual method of attaching that to fabric would be to couch the cord, meaning sew over it with finer thread.

Yes, there are needles to handle this sort of thing. If it's very soft, you might be able to use a large embroidery/crewel needle (look for sizes 1 to 3) ; if it's firm, you may need something more like an upholstery needle.
http://image.made-in-china.com/2f0j00mGQaegTbFzUp/Hand-Sewing-Needles.jpg

Couching:
http://www.embroiderersguild.com/stitch/stitches/couching.html
http://www.youtube.com/watch?v=0wW62UZMLQc
If you explain more about what you're trying to do, I may be able to help you more.

Chocolate

1c.m