Higher pressure is never unsave for the tires.
The given maximum pressure written on sidewall is the maximum cold pressure the tire-maker alows.
this is not the pressure at wich the tire is allowed to bare its maximum load up to 160km/99m/h, wich is also given on sidewall as loadindex or maximum load.
This pressure I will call AT-pressure further. For P-tires ,AT-pressure is 35psi in American system ( EUR 36 psi) .
But most likely your low Hight/Width division tires are XL/reinforced/Extraload wich have AT-pressure of USA 41 psi, EUR 42 psi.
I once got hold of the official formula to calculate pressure for lower then maximum load.
So dont be afraid of the higher pressure .
I once read that tires are tested to stand an absolute pressure of 2 to 3 times the AT pressure .
So a P-tire will blow somewhere between70 psi and 105 psi. A XL// tire between 82 and 123 psi.
Tire pressure advice is all about load on tire in ratio to maximum load , and speed you maximaly drive.
A bit about alighnment ( camber angle).
For lower speed the tire is allowed higher maximum load for the same AT-pressure .
And vice versa higher speed lower maximum load.