OP here ...

Rick said:

I split my B&D blades into the fixed & movable parts .... and simply filed
the blades with a diamond sharpening file.

And Andy said:

Strip, clean, re-lubricate, re-assemble.

They don't go blunt because they're blunt, they go blunt because
there's a gap between the blades' working edges owing to a build-up of
gunk.

***Exactly***! I do realise that disassembly is the best way (I was
going to de-gunk the blades, and then go over the cutting surfaces with
a dead flat file.)

However, the bit I'm worried about (which I didn't make clear enough) is
the reassembly: I don't want to undo the securing nuts in teh blade
assembly until I know I'll be able to put them back at the right
tension: a fraction too tight and I'll f*** the cutter, a fraction too
loose and it'll be worse than it was before.

So the recommendations I'm looking for (sorry for not making it clear
enough) are to do with disassembly and reassembly.

John

p.s. I'm not normally afraid to do this with things (dis- and
re-assembly often fixes stuff!), but in the case of a precision tool ....