Jumper wire for thin connector pin / holes
You can try using standard 24 AWG solid wire.  This is the standard size used in solid-core CAT-5 Ethernet cable and is also one of the most common sizes used in the telephone industry.  The nominal diameter is 0.020".

If the conductor is just that tiny bit too thick, try squeezing the conductor slightly with a pair of smooth-jaw pliers.  It won't take much pressure to reduce the thickness by a couple of mils.

FWIW - I use 24 AWG solid-core wire for all of my breadboarding.  It fits standard breadboards perfectly and is also a perfect fit in machine-pin IC sockets.  You get huge amounts for free just by chatting with your local Telco guys.

One final tip: I normally cut the very end (tip) of the bare conductor at an angle using scissor-type cutters (Miller type 101 Wire strippers / cutters).  This angled cut gives the conductor a taper which can make it much easier to push into a connector.