Can I put lower profile tyres on my car?

Well other than lowering the gearing not really.

The bigger question is why you want to make the change?

This.

It will lower the car quite a bit.

However, you could argue it can change the scrub radius to it having less, albeit slightly, so the car will behave differently. So it may be a little dartier etc.

Personally, I'd stick with the 195/60s. If you want less, profile, go to a 17", where the prices are still sensible in that region. 16" for some reason isn't.

It will lower the car by the small amount lost from the sidewall. The effect is visually negated by the wheels looking smaller in the wheel arches however so really isn’t worth doing to ‘lower’ it.

I just went from the standard 195/55R16 to 195/50R15 (approx. 1" overall diameter difference) on an R50 Mini Cooper, and immediately noticed improved acceleration, which makes for less 'boggy' pulling out of junctions, etc.

Car also feels more nippy and nimble, with less wheel weight to have to lug about.

The wheels fill the arches quite nicely still, however, I now have to take it slowly going over speed humps or ruts to avoid the dreaded scraping of various bits of bumper trim, etc.

Thats about it, the aim is to keep the rolling diameter close to the same size.