Have a look at the "14 cm" shorty square cuts from Speedo Europe. For example:
https://www.amazon.co.uk/Speedo-Hydr...ds=speedo+14cm
https://www.amazon.co.uk/Speedo-Mens...ds=speedo+14cm
https://www.amazon.co.uk/d/Clothing/...ds=speedo+14cm
They cover lower on the butt, where one can get a bit saggy with age. They are pretty low-waisted, but not enough to require shaving.
Nothing like them from Speedo USA, which is a completely different company. Many European sellers won't ship to the USA, due to Speedo USA licensing the trademark here. But Amazon will.