Microshift makes a thumb shifter if this will be going on a standard 22.2mm flat bar. If for drop bars, they also make a bar end shifter. They work great and would meet your multi-shift expectation.

Trigger shifters like the one you linked to are typically one-click, one-gear only type of deal.

As for the gripshifts, I don't have any experience with those but cables will stretch and need re-tensioning regardless of the shifter used. That is why it is recommended to have cable tensioners on your shifters (and as far as I know all Nexus8/Alfine shifters have this).

Stretched cables can allow the gears to be slightly misaligned, which would chew them up and eventually destroy them.