This one sounds most plausible to me, given some were discovered with coin hoards.
In the past coins used to have simple round edges. People would scrape (with say a knife or other hard tool) metal from coins slightly reducing their diameter imperceptibly.
This tool could be used both by scrapers and verifiers. After a daytime trading job a scraper might sort his coins by type, and do the pass vs no-pass test. Scraping ones that were slightly larger than average, but not those already scraped by others.
A verifier that doesn't scrape, but wants to avoid incurring loss due to scrapers might use the tool during trading and refuse coins that fall through, or he might more discreetly sort the revenue after work, and sort into coins to keep, and coins to return as change.
I don't know if Isaac Newton was the first to introduce the slotted edges to deter scraping, but he did locally introduce it when he was appointed head of the Royal Mint.