Will this old amp kill my speakers?

As long as the speakers do not distort (a sign of underpower) while playing, you know the amp is driving them fine.

Man the whole underpowered-amps-damaging-speakers thing is slung around to death on forums with little or no acknowledgment of the many extremely complicated variables at play. Catastrophic amp failure aside, I think it's usually too much power that kills speakers dead, not harmonic distortion from clipping. Still, it's important to note that an amp that's clipping can put out MORE continuous power than when playing clean...up to a THEORETICAL max of 3db (or 2x power) for a pure square wave...so if your amp and speakers are both rated for similar (honest) continuous power levels, then clipping could provide the extra power to push your tweeters over the edge.

I've read elsewhere, and agree with, the idea that if your speakers are (honestly) rated for 3-4x more power than your amp at (honest) continuous levels, then there's almost no way you're going to damage them even with heavy clipping (though I have no idea why anyone would want to listen to heavy clipping). Any more amp than that, and you're just going to have to keep a careful eye on the combination of source material level and volume control, to protect your speakers...no way around that. And the volume mark itself is no good indication of power level - it's not even a good relative measure (within the same system) because of differences in recordings. The SPL coming out of the speakers is a good relative indication - louder ALWAYS means more more power is running through.

With a vintage amp like that you have the additional concern of "catastrophic failure" due to old/out of spec parts. Get it checked up, get the electrolytic caps replaced, make sure it isn't leaking DC, etc. A full restore is always a good idea.

You can mitigate your fears by getting a nicely efficient speakers (more volume for less power) with good power handling and pairing them up with a moderately powerful (25-60 Watts), well-engineered amp

This is a quote from the Installation manual for a pair of Kef Reference speakers I own.

" If higher than specified amplifer powers are used, great care should be taken to avoid abnormal conditions such as swith-on surges or gross distortion, either of the amplifier or the speaker, resulting in power peaks greatly in excess of the ratings specified. Care should be taken as the possibility still exsists under certain conditions (such as excessive bass or treble boost caused by tone and/or loudness controls, graphic equalisers, etc.) that the speaker can be overloaded or damaged. The lower limits of the amplifier power are those necessary to give a resonable sound pressure level under domestic conditions.

Remember it is easier to damage loudspeakers by using a small amplifier driven into distortion by too much volume possibly with bass and treble boost, than by using a larger amplifier which has power in reserve. If in doubt ask your dealer"

With Mulveling stating
"I think it's usually too much power that kills speakers dead, not harmonic distortion from clipping"

And the Kef Manual stating
"Remember it is easier to damage loudspeakers by using a small amplifier driven into distortion by too much volume possibly with bass and treble boost, than by using a larger amplifier which has power in reserve"

Could someone with the knowledge of "why" chime in

The following article may help explain.

Clipping Does Not Blow Speakers