Welcome to the forum!
Soldering a pigtail to most PCMCIA wireless cards isn't too difficult, just bear in mind you want a very fine tip soldering iron and it helps have have a bit of soldering experience. Unfortunately the photos are a bit small to pick up any detail on. Are you able to post a higher resolution picture? If so I could draw some diagrams on it. Placing the card on a scanner will do the job nicely.
Follow the tracks from the antennas (those gold 'C' shaped designs on the end) and you should find each one leads through a tiny chip capacitor into a small 6 or 8 pin surface mount IC.
Many PCMCIA cards have solder pads for external connectors as well as inbuilt antennas etched on the PCB, and you can solder the pigtail directly to these pads. You might need to solder the capacitor into a different position to direct the signal to the external connector instead of internal one.
If yours doesn't have provision for external connectors then you will need to cut the tracks near the inbuilt antenna
before it gets to the capacitor, scape some of the green solder mask off and solder the pigtail directly to the track.
Quite a few PCMCIA cards only seem to transmit using one of the two antennas. If one is labelled
Main or similar use that. If they aren't labelled, you might need to try connecting to both to see which one gives the best performance.
I did this to a Senao card once and even though it already had an external antenna connector the process is pretty similar. View pictures
here
If you have some higher res pictures that would surely help.