Klipsch and Capacitors

Probably not on that model as the only electrolytic cap is on the woofer.

I'd play them for 200-300 hours and then consider updating the tweeter diaphragm's (Titanium?) if more clarity/less bite is desired.

After that maybe the crossovers starting with air-core inductors.

DeKay

Leave the speakers alone. Some playing time to loosen up the drivers is all you need.

Thanks for the advice! 

+1 for only electrolytic caps are likely to wear over time.  

There's a large cap on the woofer.  If that's electrolytic you should be careful replacing it with a modern as the difference in ESR may be significant.  

For the tweeter caps I might suggest you try an Audyn 0.1uF TruCopper bypass.  About $20 each.  

@maprik ,  I have to ask.  How did a pair of KG4s go unused for 40 years?  I have 2 pairs BTW.