The folks at the Cutler's Company have always been very helpful where it was possible. Their contact page is here.
You should definitely hone and use it. It's an extraordinary feeling shaving with such an old razor!
And sorry to have been so brief earlier, I was in the middle of things and pretty clearly wasn't able to be clear enough about the marks.
Yes, the books of marks that the Cutlers Company keeps are the definitive source on Sheffield marks. However, I have not seen the dart & pipe mark as it was recorded in their books. The only sources I've seen on it are the marks as recorded in Sketchley's directory (as seen on Fikira's excellent page), and the marks on razors.
Of the three or four 18th century marks I've gone to the Cutler's Company to get help with, none remained with a single family.
Experience has shown me that the marks as recorded in the directories are often wrong in small and large ways. Mirroring of that sort is common. That is, the mark they've recorded in the directory has reversals or even missing characters from the mark as it was recorded in the mark books and on goods. However, the directories are as good as we get for knowing who was actually working. The apprentice registries are not a good indicator. A cutler who completed their apprenticeship had no guarantee of selling their own goods -- that depended entirely on having the money to set up shop somewhere, and in the late 18th century, more often than not that meant renting space in one of the many larger wheels or having the resources to build your own workshop, which is not very likely for most. Most of those who completed their apprenticeships went on to work for another cutler.
Another note on families and the apprentice registries -- Leader's gigantic second volume of the Company's history, the one with the apprentice registries, is a pain in the butt to actually make use of, partly because Sheffield family names made matters difficult even with access to primary sources. Your note of William Bradshaw and three dates of freedom, for example, is probably referencing three different William Bradshaws. Possibly all directly related, but maddeningly, not necessarily. There were three different men named Sleigh Rowland all working in Sheffield at the same time. Two of them were in the same branch of the trades. They were, at best, second cousins.
It would be very, very odd for a general cutler to be freed three separate times over the course of 25 years.
The Bradshaw entry in the apprentice registry is an especially bad mire because of how expansive the family name was. While they were all likely distantly related, without talking to descendants, I would not assume they all thought of each other as relatives.
I can't turn up anything in the way of plausible birth or death records for a William Bradshaw to be apprenticed to John Hoole in 1730 (he would've been between 7-12 when apprenticed and his apprenticeship would have been for 7 years).
However, I did turn up a baptism of a William Bradshaw, son of William Bradshaw (cutler) in 1734. That timing works out very well to suggest (1) William Bradshaw, freed in 1730 to father William Bradshaw, freed in 1752. The 1755 freedom was probably a cousin... But finding records for folks in the early parts of the 18th century in Sheffield is a challenge. Some were lost in WWII, some were just not recorded. Some were recorded and lost in other ways. Some were recorded and haven't been digitized. The best way of finding people is headstones, but even there you run into numerous entire churchyards which are gone as well as the headstones, and even when present, many 18th century and even early 19th century headstones in Sheffield are actively difficult to decipher from the centuries of weather.
Helpfully, John Hoole is a little more traceable!
Attachment 296469
And this is almost certainly his death, despite the different spelling.
Attachment 296470