Replacing tweeter in vintage speaker

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I have a pair of vintage speaker systems, of which I'm considering a modification. I think the sound is very good, but sometimes it's overly bright, and sounds like "s" can sound somewhat sharp. Therefore, just hypothetically at first, I'm considering replacing the tweeters. It's also a good thought exercise, as my DIY audio experience includes little on speakers.

Anyway, how do I proceed? I don't know any of the specs of the tweeter, accept it's nominal impedance (8 Ohm), and the manual states that the entire speaker was meant to be used with amplifiers with a maximum of 60W. The manual doesn't say much more, unfortunately.

To determine the usable frequency range, I can measure the crossover output. When doing so, does the -3dB frequency comply with the -3dB frequency of the tweeter?

And I suppose the efficiency of a replacement driver will have to match. I do have an SPL meter, so I should be able to make an approximation of the current driver's efficiency.

How important is the resonance frequency of a replacement driver? Does it need to be an exact match?
 
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