I ended up buying a CCrane SWPocket radio:
http://www.ccrane.com/radios/shortwave-radios/ccradio-swp.aspxI chose it mostly because they have a good reputation and they are a local company. It runs on two AA's for allegedly 70 hours, although I won't push it anywhere near that long when wanting to record. It has an external antenna and best of all for me, it is quite a bit smaller than I thought it would be from the photo, so I can keep things compact and simple. Anyway, time will tell how well it works but I am optimistic.
What was mentioned about using the headphone jack on a FM Walkman for patch cords and hence losing my antenna makes sense - it got pretty good reception but anytime I had to move it or otherwise mess with it, I tended to get reception problems. I'll have to use the headphone out jack on the radio I bought but since it has a separate external antenna, I assume this will no longer be an issue.
Thanks again for all the input - I'll keep you posted on how it works.