If the thread itself is dodgy it’ll need a proper tool, the cut BB trick can chase dirt and paint and even swarf out of a good thread but it won’t sort a bad thread (since your “tap” is made of softer metal than the BB shell)
I just ran a hacksaw across mine about 8 times round the circumference… I find that clogs up very easily but, on the plus side, that prevents me from being tempted to force it. I reckon wider cuts would probably clear better though but never really felt the need to try it- not really something you have to do often.
But obviously if you hurt the thread you’ll regret it so if you’re unsure, worth taking it to a good LBS IMO.