Matt, I use a potassium ferricyanide and potassium bromide rehalogenating bleach for just about everything and it works just fine. I like it because it is reversible to some extent and seems to be more controllable. Farmer's reducer type bleaches use potassium ferricyanide and sodium thioisulfite (hypo) and are not reversible. Some workers use just a ferricyanide solution and rely on carried-over fixer to provide the catalyst. In any case, the prints needs to be thoroughly rinsed and refixed after bleaching. I'm not really sure why refixing is necessary with Farmer's reducer, but everything I've read (including the Darkroom Cookbook) says to refix after bleaching with Farmer's formulae. Certainly you need to refix with a rehalogenating bleach. See here:
https://books.google.at/books?id=Ba_OCwAAQBAJ&pg=PA129&lpg=PA129&dq=farmer's+reducer+instructions&source=bl&ots=wOaNWehrNc&sig=mlakaio8Y25GHCJYxXRy4bf8MEc&hl=en&sa=X&ved=0ahUKEwi98Pqw49XSAhXMaxQKHbGjA544ChDoAQglMAI#v=onepage&q=farmer's reducer instructions&f=false
Andrei, Bleach from a sepia toner kit is a ferricyanide/bromide rehalogenating bleach. It will work just fine for bleaching prints without toning afterwards if you dilute it properly (i.e., weaker). After bleaching a print, either locally or overall, you need to rinse it well in running water and then refix it.
Best,
Doremus