From my own experience I have never had any problem with old (and I am talking about 30 year old) chainsets with new chains up to 9 speed. There is a potential concern that the narrower chains can slip in between the chain rings, but as
Sheldon said it seldom creates any problem even for 10 speed chains. Perhaps one reason why it usually works fine is because old chainsets seldom have adjacent chain rings with large teeth difference.
For completeness, there can be problems in squeezing a 7/8 speed chain into a higher speed cassette. I looked into and eventually experimented with a Campag 9 speed cassette and found it
ok albeit not ideal. However such chains are most unlikely to work satisfactorily with 9 speed Shimano cassettes because they have narrower pitch.
ps As usual Porkypete is right - old 5 and "standard 6" speed chains were 7.8mm wide, as opposed to the more recent 7.1mm (IG) to 7.3mm (HG) 7/8 speed chains commonly used nowadays for 5/6/7/8 speed.
pps Regarding "splaying the rear stay to fit" the frame should be steel and not more exotic than 653.