Where to buy zinc-less hardware (nuts, washers and bolts)

Any of your listed stores should have stainless steel hardware which I think is the only solution to your requirement.

Check fastenal.

All three should have what you are looking for.  They usually put up the most common sellers on the displays. They do have drawers with speciality items. Ask an employee and they should be able to find what you are looking for.  You can always try ACE hardware.  I am sometimes surprised how much they stuff into their stores.

Ace Hardware will be your best bet, or a TrueValue

Is there any place around you that sells boating supplies? There always good for stainless steel hardware.

I did build my raised grill w. stainless bolts, etc. from a True Value shop. But in an ensuing discussion, fishlessman, who runs a welding shop, said that the zinc cladding was a very minimal risk.

While zinc vapor is dangerous, the hazard from metal work is very small. Get stainless if you can find it, easier to clean,  but zinc clad can be used.

What @henapple said. My local HD doesn't carry a lot of ss nuts /bolts / washers. Lowes carries more in those cabinets where the other nuts and bolts are. I've seen them at Ace too, but they were more expensive.

If you cannot find anything locally, McMaster-Carr carries just about anything you might need.  Excellent service from them over the years.