Safely use 10A Laptop charger Plug?
It is simple really, the marking on the plug refers to the plug.
So the plug (only the plug) can handle 10 A, 250 V. That does not mean that it will take 10A. It's just that it can handle it. The adapter detemines the current and it will take no more than 1.6 A.

The markings on the adapter refer to ... you guessed it, the adapter.
The adapter will take 100 - 240 V with a maximum of 1.6 A as input.
This is the rating for which it will operate. You could give it 90 V but then it is not guaranteed to work. It needs at least 100 V but no more than 240 V.
It will not take more than 1.6 A. So the plug is OK, since the plug can handle up to 10 A.

The adapter's output will be 19.5 V and the maximum current you can load it with is 4.62 A.

So: stop being concerned ! What you have there is perfectly normal.