Difficult one to answer Onyx, you can do it yourself if you know what you are doing, but if not you'll need a man who does.
You need to take the propsahft off to even get near the internals of the handbrake, getting to the cable is fiddly, but not difficult. If you have the right tools it is all very easy. whip off the rear prop, pop off the drum, clean it all out, put in new shoes, drum back on, adjust up and prop back on.
Things that can go wrong,
Prop bolts rounded, adjuster seized, drum knackered, cable stretched.....
Have you had a look in the Haynes/Land Rover manual yet?
graham