If I go to a shop they will laugh at me...
The reason is that my parts (watch screws) are so tiny, about 1mm
long.
I would try electroless chemical polishing at home (I don't have more
that 6 at a time) but I don't know the composition of the acid bath.
Can you please help?

Sorry, can't help with electoless polishing. What makes you think a
shop hasn't seen lots of stuff like your screws already? If you are
lucky they will relish the challenge :-).

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Regards,
Carl Ijames carl.ijames at verizon.net