I don’t see any other answers, so I’l give it a shot.
As far as I know, the amplifier in the KLH Model Twenty and Model Twenty Four music systems were rated at 30 wpc IHF, so it’s a good bet they are the same amp. (BTW, IHF is different than the RMS wattage rating in use today. 30 watts IHF is probably closer to 10-15 watts RMS.) I’m not sure about the Model Twenty Six music system, but KLH tended to repackage their amplifiers for use in all their music systems. I'm reasonably certain that the amp in the Model Twenty music system, the one designed to power the Model Twenty, 4 ohm speakers, is pretty much the same as the amp in the Model Twenty Six system.
I owned a set of Model Twenty 4 ohm speakers from a Model Twenty music system “back in the day”. It was my main speaker set from 1971 until about 1980. I used all manner of amplifiers and receivers to power the Model Twenty’s and never had a problem. Most amplifiers and receivers can power a 4 ohm load without a problem, and I don’t think the KLH amplifiers are an exception. The only thing you cannot do with a 4 ohm speaker is pair it with another speaker set and try to drive two sets of speakers at the same time. The load on the amp then drops to below 4 ohms, and almost all amps will have a problem with that.
Bottom line: You should not have a problem driving the Model Twenty speakers with the Twenty Six amplifier if the amplifier is up to specs. That’s not a written guarantee, only because you’re working with an amplifier that is probably just under 50 years old, and it could be significantly under its design specifications. Try plugging the speakers into the amp with RCA plugs connected to some speaker wire. Listen at low volume and try to hear if there is any distortion. Slowly increase the volume and carefully listen until you are at a moderately high volume. If you are concerned about the condition of the amp, bring it to a tech for a once over before trying the Model Twenty speakers.
BTW, have you changed the capacitors in the speakers and sealed the cloth woofers? KLH capacitors are notorious for going bad over time, and if the woofers are not sealed the bass performance of the speaker will be seriously compromised. If you need a sealer, let me know and I can recommend the only sealer you should use.
Good luck, and let every one know how you make out.