A 35 ft. antenna should bring in most of the SW bands well. Longer lengths may bring in the lower SW bands better. A higher antenna will bring in signals better than a low one.
Like the other guys have said, an external antenna may overload your portable, depending on the overall signal strengths that occur where you live. Where I live (NW US) you can attach a 100 ft. wire to many portables and have few problems. Other areas of the US, where there are higher SW signal strengths, that could be a problem.
As for the braid, you could attach it to a ground wire and use it as a radio ground (some SWLers swear by radio grounds, others don't see much difference in using one). Or you could just tape it off.
One thing (and you probably already know this) is to be careful during stormy weather or dry winter air conditions with an outdoor antenna, when things like lightning and static can wreak havoc on a radio.
Disconnect and ground the antenna during storms, and if there are dry winter conditions some sort of safety connection between the antenna and the ground is a good idea, as static can zap a radio's RF amp transistor (some guys use a big resistor between antenna and ground, other guys use a pair of diodes wired back to back between the antenna and ground).