I work with low voltage electronics professionally and anything with a motor attached will just run so much smoother if you have a battery in it. Replacing the battery is in general not difficult, but fiddling around with these things is always dangerous.
A short circuit on a modern Li-Ion cell can cause the cell to explode like a small grenade. Never wear any jewelry while you work with them, never have anything touch both contacts at the same time, always have an open window through which you can throw any burning batteries.
If in doubt, don't fiddle around with it.
That said, there's a variety of systems you can change from battery to wired with very low effort. Something like a TV remote, an alarm clock and everything like that is easily converted and safe to do so. (basically anything where you can take out the batteries before you start meddling).
AA and AAA batteries come at 1.5V, so just Chek how many are in series and multiply that with 1.5. That's the socket plug you need