I have had a look on other entries on here and can add a bit of useless info.
It is fine to dismantle the compass - do it carefully.
It is easy to remove the battery with a soldering iron
It should be easy to solder in a new battery
 
Main problem - I cant find the correct battery ML2430 HZ1 - seems hard to find in UK
 
But the ML2430 HS1 is available - two ordered for about a fiver each - 
 
The difference is the soldered on pins but looks easy to modify.
 
Has anyone actually replaced a battery with success! 
 

I haven't yet, I've got the same two batteries on my desk ready to fit- been there for 6 months already and I haven't got around to it.  The 'issues' with replacement seem to have been restarting the tacktick after the battery change on some units. I was planning on just clipping off one of the contacts.
 
 http://www.vanaheim.co.nz/compass.htm
 
Some early units seem to have had a jumper on the circuit board  to switch it off. As the article says - if its unuseable anyway there's nothing to loose.....

The hardest bit is finding the batteries. I've used some equivalents that are readily available in the uk but are physically larger.
You'll need a good solder sucker as the pads are well loaded. Just watch out not to damage the LCD displays during the process.
Otherwise follow the informative link in Kieron's post. 
I've not had problems with restarting the 4 units I've dealt with. 
There really isn't anything to loose as the unit is scrap with no battery.
Good luck with the repair. It's not hard to do.

battery soldered in.Started immediately.No excuses left to out smart Dan Alsop or JonTurner in LymeBay!

Must try mine now! thanks Stuart