I think people make too much of the mil-spec name...
What you want is REAL para-cord.
I sometimes buy mil-spec and sometimes just go to the source and buy from a rigger's store...
They have REAL para-cord in MANY variations.
If you need thinner, they have (I think) down to 4 strand. and I really like the 10 and 12 strand stuff.
That stuff is STRONG!

You do want to be sure that you get the REAL para-cord though...
A lot of what is sold does NOT have the inner strands that are each made up of two even smaller strands.
Some just has the fibers(unstranded) inside of the outer covering. This CAN be strong, but there is no guarantee...