No, I couldn't disable it as there was no alternative graphics hardware on the motherboard.
LatencyMon (not Checker, my mistake) was showing dxgkrnl.sys and the NVIDIA kernel mode driver were causing spikes which coincided with clicks in the audio. I searched for info on this and found it to be a reasonably common issue with NVIDIA hardware (I had a GTX 950 installed). So I tried a variety of settings in software and bios to try and alleviate it but with little improvement. In the end I bought a cheap Radeon card, installed it and immediately had an improvement without extra tweaks.
Now this result may be specific to my use-case and the software I was using on my Windows 7 box. I use virtual instruments and effects in
Reaper audio software with realtime MIDI and audio streams, so it may be more demanding than other audio use-cases. It may be that I didn't troubleshoot the problem exhaustively enough and some other element was not playing happily with the graphics driver and delaying procedure calls. But in the end, changing to the Radeon card simply made the problem go away.
On the other hand, I have had an NVIDIA card in my Win7 audio PC at work for years without these issues, but that is a whole different set of hardware and software involved . . .