Just had another thought. Something else that changed when I installed the last Security Update (when this problem manifested), was that the NVidia CUDA Driver became outdated, and there's no newer version.
I can't seem to find a definitive way of getting rid of it, but I wonder if processor cycles are being intercepted by that (in a totally uneducated way of explaining what I mean).
NOTE: I have switched to an AMD Vega64-based card, and things are indeed working much better. Some niggling things with the NVidia card are gone. Your mouse issue may be related to just having an NVidia card in the system. Which, IMHO, completely sucks.
Doh! In the continuation of the freezing mouse saga, I was getting SO fed up with it this morning, I was on the verge of moving to High Sierra. The thing that is stopping me at the moment is that this is a production machine, and work is so crazy at the moment that I can't risk the downtime. The freezing was really hampering my work, though. Past googling had suggested lots more people experiencing the same problem but with Logitech Bluetooth mice. Mine is Logitech, but wired, and the replacement I'd bought thinking the mouse was at fault was the exact same model as they're my favourite of all time. Upon reading that Logitech knew of problems with Sierra (and maybe I was lucky that I'd not experienced it until the last Security Update) it occurred to me that maybe it was worth trying a different brand.
One Amazon Basics mouse later, and I'd had a few hours of problem-free pointing. I didn't like the feel, so have gone for a bigger HP X500, and that too – so far – hasn't seen any freezing.
Who would have thought that a simple USB wired mouse could have these kind of problems?! I'll update as I spend time with it.