I'm not familiar with that Sony, but most portables tend to overload with larger antennas. However, you won't know until you try (or someone else can confirm)
You could test this cheaply by just finding a small roll of wire and running it along your fence before you make any large-scale purchase.
Any horizontal antenna that low to the ground won't have the directional properties of those that are usually designed to operate 1/2 wavelength above ground. It doesn't mean it won't work, I just wouldn't be too worried about placing it east-west since being that low to the ground the directional properties would be very random in the azimuth plane, and most likely very high in elevation.
But you gotta' start somewhere!
Much of it depends on how interested you are with HF antennas. This could be the first of many random wires, end fed wires, center fed dipoles, off-center fed dipoles, verticals, loops etc.
I say give a cheap random wire a try, and if it doesn't overload your Sony, enjoy the new reception, check out the antenna wiki's and swl / amateur sites, and start thinking about your *next* one. Repeat as necessary.
Antennas are a blast and can be somewhat cheap to homebrew....