Yes a backpack and with a wfp is good enough to get started for sure.
Blackwash is just 10% sodium hypochlorite (also called hypo or SH for short) with a scent & soap already added.
Regards to cleaning cobble block with SH I take it you mean block paving. If so then yes it will to a degree depending on how strong you make the mix, dwell time etc. However SH will not remove weeds, moss etc from the joints like using a descent pressure washer with a turbo would but will turn the weeds, moss etc white and a bit easier to remove by manual methods.
It seems more common now to use SH after pressure washing or even before if you know what you are doing to help remove stubborn black spot etc for a cleaner looking finish.