Best way to solder a small 10 pin connector

I don’t think hot-air & solder paste is actually the right tool for this.
I do have some advice though:

  1. Get some magnification, it will help a LOT with soldering small parts. Actual suggestions can be found here: The Magnification Observation
  2. If you need it, get some “helping hands” or something to hold the pieces while you solder. Some recommendations: The Holding Help
  3. Try to use the right amount of solder so that it doesn’t overflow onto other pads/components. Thin solder wire helps with this. (The one I use is 0.5mm.)
  4. As long as your iron isn’t too hot, so that it damages the board, you can always re-do any soldering that you mess up. After you solder it, check it with a multimeter to make sure that you have connections where you want to, and no shorts, and if it doesn’t work correctly, just fix it. You may need a solder sucker and/or some solder braid for the fix though.

Generally speaking, the only thing you can really mess up on a pogo pin board is the pogo pins themselves. If you get solder into the mechanism, or you bend the pins, then you’ll need to get new pins, but hopefully you can get those from digi-key, mouser or somewhere local.