Bar Keepers Friend often doesn't even need scrubbing at all, to remove light rust. Just mix it with some water to make a paste, then apply it to the affected spots with a Q-tip. Let it sit for 30-60 seconds, then rinse it off. The oxalic acid in BKF does the work, dissolving the iron oxide (rust). So long as it's not left on the steel too long, there's little risk of altering the finish. Leaving it longer than ~60 seconds or so runs a risk of etching the steel.
This^ would be my first go-to, for rust on a blade; especially on a stainless blade. It's just easy. The 'specks' of rust on the blade, per the OP, should be simple to remove this way.
David