Replacement 10", 35 watt, 8 ohm speaker?

You'd get sound.

Seriously, the power rating of a speaker refers to the amount of juice it can take without distorting (or in the case of my old stereo speakers, blowing little bits of speaker paper all around the room in one big "pthwack!!"

You probably have a speaker rated for quite a bit more than the averaged output of the amp. Maybe some ee type can get on this thread and explain HOW it works. I just understand THAT it'll work.

So running a 50 or 60, or even a 100 watt rated speaker might sound great with a 30 watt amp.

You do have to match signal impedance, though. Can you get any information about the impedance of the old speaker? It's likely to be 4 or 8 ohms, and there's a go / no go kind of difference there. You do not want to mismatch the resistance of the circuit with what it was designed to encounter.
 
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