Chain skip options on vintage 'frankenbike' I have a late 80s Bianchi Volpe which came with Sakae Ringyo SX cranks and bb, SunTour barcon shifters and derailers, and SunTour chain. 

The freewheel was aftermarket 7 speed and never rolled well so I replaced it with a Shimano 7 speed available at my LBS. 

Everything was working well and the drive train was low noise and decently shifting despite the frankenbike nature and problems others have had, specifically that SunTour shifter throw and cage travel is not SIS compatible. 

Recently I replaced the chain with a SRAM 9 speed based on reports that the narrower chain is even better on noise and can confirm, drivetrain is much quieter. 

But now the chain skips under load. I know cog wear can be the source of this skip, but neither the chainwheels nor freewheel appear to have that high wear, and the original chain was only a few hundred miles past the Park Tool's ".75" indicator mark.

Attached is a picture of the filthy cranks (Chicago winter salt and sand included).

If I do need to replace the two largest chain wheels, must they be SR? Other brands seem more widely available, assuming BCD matches.   

Edit: Picture for real this time.
Dirty freewheel:
First, I'd trouble shoot why the chain is skipping. Does it only happen under heavy load? Does it always happen in the same place (maybe a stiff link)? Does the derailleur do something funny? 

If the BCD and bolt pattern matches, stick whatever chainrings you want in there (subject to front derailleur constraints on chainring size + tooth gap). As for if your chainrings are worn or not, the picture isn't there, but there are plenty of other questions (see sidebar or search) on this SE to check if your chainrings or cogs are worn beyond. 

While using a 9 speed chain on a 7 speed cassette should work, it will likely be a bit sloppier than using a 7 speed or 8 speed chain (they are narrower than the chains that the 7 speed cogs were designed for). They're also pricier. So, I'd also go back to a 7/8 speed chain in the future. 

The change from Suntour freewheel to Shimano freewheel shouldn't really have caused any problems other than maybe some minor adjustments (unless you're running a microdrive drivetrain).