Fred A. Will opened his cutlery shop in 1863.

While not common, there have been a few corkscrews dicovered, that are marked:

FRED. A. WILL arched over S. F. CAL.

Jacob Herman Schintz also opened his own shop in 1863. When found, his corkscrews are usually marked J.H. SCHINTZ or alternatively J.H SHINTZ atop SAN FRANCISCO

In The Knifemakers of Old San Francisco, Levine writes:

For a loyal Californian to open a bottle of good California wine, not just any corkscrew woud do.  He had to use a California corkscrew or the wine would not taste right.  At 10 Stevenson Street, therefore, J. H. Schintz’s California corkscrew business prospered

Schintz made corkscrews of every quality, from the plainest wooden handled models to the most ornate mounted in walrus ivory and decorated with silver and gold.  In the early 1870’s, Schintz also continued to make cutlery for Price and to supervise Price’s employees.  Schintz might have even have made some corkscrews on contract for Will & Finck.

From the World Class Corkscrew book:

The Teackle bar set. Three bar utensils created by the early San Francisco cutler Michael Price and bearing his maker’s mark. The corkscrew, bar knife, and cutter/ice pick have walrus ivory handles scrimshawed with the name E. W. Teackle. In 1864, Elisha Teackle was known to have shot a man in San Francisco in broad daylight on a busy street for having insulted his wife, though nothing apparently came of the case. This set was created c.1868. The corkscrew was separated from the set at sometime in the past, but through a series of fortuitous events, was reunited with the other two pieces. Jack Bandy Collection

Julius Finck was a cutler from Baden German, who arrived in San Francisco in the 1850's, and in short order joined Fred A. Will to form Will & Finck.

Reknowned for their bowie knives, their firm became one of the more prosperous cutlers of the time, and carried a myriad of wares.

Their corkscrews have turned up with a few different marks, either with WILL & FINCK, S. F. CAL in a straight line down the shaft of the corkscrew, WILL & FINCK arched above S. F. CAL. WILL atop & FINCK, and WILL & FINCK CO.

M. Price, J.H. Schintz, and Will & Finck all had showrooms, so by default, they sold the corkscrews that they made (and a few that they didn't). However, in Bernard Levine's explains:

Of those cutlers who advertised that they made cutlery to order, most actually had their new work done by others. Several, such as B. Nathan & Co., George C. Shreve & Co., and Haynes & Lawton, had some of their special cutlery made by Will & Finck.

Elsewhere in his text, Levine does mention other retailers of the era:

In San Francisco directories, and in other early sources, are dozens of names of cutlers, cutlery importers, and cutlery retailers. Many of them no doubt sold razors, knifes, and scissors made elsewhere but marked with their own names. In addition, some of San Francisco’s many hardware and sporting goods wholesalers distributed knives marked with their own company names or trademarks. Frequently encountered are knives marked; Pacific Hardware and Steel, Adolph Blaich; Justinian Caire Co.; and Miller Sloss and Scott.

My assumption, shared by a couple of other collectors, is the Justinian Caire Company corkscrews were also Will & Finck production--with the J. CAIRE arched the same way over S.F. CAL that we see, at times, with Fred A. Will and Will & Finck.

In our collection we have a turned wooden handle direct pull marked J. CAIRE, S.F. CAL.

Pictured in the World Class Corkscrews book, there is another J. CAIRE shown, from the collection of the late Jack Bandy.

The World Class Corkscrews book reads as follows:

Ivory handle corkscrew marked J. CAIRE/S. F. CAL on the shank. Justinian Caire was in the hardware business in San Francisco. He was born in France in 1827 and moved to San Francisco in 1851. Jack Bandy Collection.

Levine expains that B. Nathan Co., as well as other retailers had their wares made by Will & Finck.

This example is marked B. NATHAN, this corkscrew has a facted shank, much like Will & Finck, and has a nicely turned walrus ivory handle.

This example is also marked B. NATHAN, but has a round shank, and includes a blade.

Coming soon