There are 4.8, 5.5, 6 and 6.5mm c mount lenses available on fleabay. All but the 4.8mm are for 1 inch sensors, close to S16mm.
The 4.8mm is on its way to me and may be for 1 inch. The distortions are impressive, but the 6.5mm is almost tolerable.
The best rectilinear, moderately affordable, extreme, wide angle lens in C mount, is the Kowa or Navitar 6mm HC series. Some second hand ones have wandered onto our fave electronic flea market. There appear unused. Some seller has compiled all the available video demonstrations of this lens, in the advert. Modesty forbids...
Brand new, the Kowa actually have a wider lens: 4.7mm F/2.4 for a mere $1,079 AUD. Unknown how it draws.