Do you think I would be less safe in such an airplane, or would some
extra training be sufficient?

The insurance companies are not charities. The fact that the
insurance will cost you a bundle tells you that at least the insurance
company considers you less safe at low time, even if some chat members
don't.

Faster airplanes require more planning in advance for let-downs, etc.
and the slippery airframes give you less time to recover in IMC if you
lose it for a few seconds. Lots of people would likely consider this
a cop-out, but a first class autopilot should be high on your list.