Don't short the resistor. First, the likelihood of a resistor going bad in some subtle way is exceedingly low. If it's been overheated or mechanically damaged, it will be obvious. Second, the sound chip's output driver is not particularly robust. That 10-ohm resistor is actually important.

To test the speaker itself is trivial, either with an ohmmeter, or with a DC source (eg., a battery) in series with a suitable current-limiting resistor (say, 1kilohm or so). Contact will cause the emission of a click/scratch sound out of a working speaker.