I have a DeWalt DC390 18v cordless circular saw. This takes 165mm
diameter blades on a 20mm arbour. I can't find any blade finer than
30 tooth to fit this saw. I have seen a Trend 48 tooth blade that has
the same size arbour (20mm) but is 160mm diameter (5mm less).

I have 2 questions. The first of course is if I fit the smaller Trend
blade, will it be dangerous? Secondly, will it give me the fine cut
that the blade is designed for?

Whilst on this subject, am I right in thinking that the smaller the
blade diameter, the fewer teeth are needed for finer cuts? For example,
the trend described above has 48 teeth around its circumference. This
gives 0.095 teeth per centimetre of circumference. On a 300 mm diameter
blade, to get 0.095 teeth per cm you would need 90 teeth around the
circumference. Which is a "fine" or even "extra fine" cut if
you read the adverts. Is this sort of conversion the right thing to do?