If you've only got four, why would it matter?
205/45R16 has a radius of 11.63 inches
205/40/R16 has a radius of 11.72 inches
Feck all in it.
Ony thing I'd say is it may not let the boot floor sit flat.
It took me a whoile to figure out that my boot floor wasn't flat because my 172 wheel width was more than the depth of the wheel well.
You'll be alright then as long as the wheel fits.
195/45/16 = 58.19cm diameter
205/40/17 = 59.58cm diameter
Less than 1.5cm difference compared to a 172 wheel so I'd assume it'd be all fine. There are a few ridges in the bottom sides of the wheel well I think but doubt they'd cause trouble.
He wants a 17 not a 16.