Passive pickup polarity ?

Have a cheap under saddle pickup ordered for a home built travel concert. It comes with a 3.5 mm plug for connecting to the output jack. Wire is also way too long for this application. Is there a problem with cutting off the 3.5mm pin and soldering directly to the jack. Will allow a much smaller hole at the bridge also. I am assuming that polarity on the pickup is unimportant. Is this correct?

Ron,
There is no problem with shortening the pickup cable.
Providing the output jack has solder terminals (and not an integrated 2.5mm socket), all my installations get the snip and are soldered.
The polarity is important.
When you cut the cable, the innermost conductor should connect to the centre connector of the jack.
The outer braid (co-axial shielding) must connect to outer connector of the jack. If you invert the polarity, you will still get a signal, but are inviting extraneous noise issues from stray EM sources.
The aim is to keep the shielding continuously earthed from the pickup, through the amplifier, to the mains socket and beyond.

Bazuku, Thanks for the reply. Had not thought about the shielding issue. Will proceed accordingly.