... well, I could until the battery packed up.
Fortunately replacements are easy enough to source from the internet and fitting isn't too scary if you have ten minutes and a trusty blade.
Step 1. Use the trusty blade to prise the top off the iPod. It's held on by glue and should peel off without too much trouble. Just be sure to note the position of the HOLD switch when you take the top off as the switch top will need to match the switch position when you reassemble later.
Step 2. Undo the two small Phillips screws.
Step 3. Similar to step1 - but this time prise off the bottom of the Mini. Again, it's held on by glue.
Step 4. There are four springy clips holding the metal base in place. Bend them slightly inwards one at a time and....
Step 5. ...hey presto, the metal base lifts out.
Step 6. Gently lift out the connector that does a fine job of connecting the thumbwheel to the PCB.
Step 7. Carefully slide the guts up and out of the casing.
Step 8. Flip over the PCB to reveal the microdrive and battery.
Step 9. Lift up and disconnect the battery.
Plug the new battery into place and reverse the procedure to reassemble. When sliding the PCB back into the case, do so gently and without forcing it as it's a tight fit and there is the risk that a tiny surface mount component could get swiped off the board. Again, check the HOLD switch is aligned with the button top when refitting the top of the Mini. The top and bottom should re-adhere to the glue that originally held them in place.
Dammit, Dan's started humming some stoopid Slade tune.... I'd better get this thing on charge...