Fine wire for breakout board soldering that won't break
As a general rule, any direct wire-soldered-into-PCB connection is prone to mechanical failure at the edge of the solder joint, if it is allowed to move at all. This should be avoided, unless mechanical strain can be relieved off the joint, and even then I would avoid it, depending on the product context.
For reliability and repairability, you would want some sort of PCB screw terminal, or a connector system with crimped wires and a header soldered onto the board. Some sort of termination that isolates the solder from the wire.
A 50-thou connector on the PCB would be compatible with a small 1.27mm JST or Molex PicoBlade etc.
Stainless steel wire? That's a strange thing to be using in any electronic application.
It isn't solderable under normal conditions, and to terminate it reliably you would probably want to use a screw terminal. At high currents, differential thermal expansion will make the joint become loose and potentially catch fire (this is a well known problem with old aluminium wire in buildings, terminated into copper connectors) and therefore terminal blocks made out of stainless steel would need to be used.
In a corrosive environment such as a marine environment, just use ordinary copper wires, maybe tin-plated copper, and use appropriate enclosures, sealants, gaskets, conformal coatings etc. Stainless steel will cause you no end of trouble.
Wire with very fine strands tends to be more flexible, particularly if silicone rubber insulation is used. This can make it less likely to put stress on the soldered joint and break.
Adafruit sell some nice little spools of thin, flexible 30AWG stranded wire, tin-plated Cu, in a range of colors.