Klipsch and Capacitors

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.

If it was me ALL the old stuff inside would be replaced with modern components.

Crossover

Terminals

Wire

Add additional dampening if needed.  But heck, that's the way I am.