Finally found a combination of software that works. For anyone that doesn't want to waste an afternoon, instructions below. This is for Win7 x64.
1) If you've plugged the scope into your computer but failed to load the driver (Unknown Device), remove it from Device Manager, then disconnect from USB.
2) On the scope, make sure the USB port is set to identify as USBTMC and not a Printer (User button, page 2 of 4).
3)Install .NET framework 3.5 SP1 from Microsoft. Needs a reboot.
4)Install NI-VISA-5.4
Runtime from the link below. Needs a reboot.
OS drop down: Windows
Version drop down: 4.5
Included Editions drop down: Runtime
It's a 73MB download.
If you go for the Full edition it's a 639MB download, but you don't need this edition.
https://www.ni.com/en/support/downloads/drivers/download.ni-visa.html#494653 5) Install EasyScopeX – V1.01.02.01.20 (Release Date 06.07.18 ) from the link below.
https://www.siglenteu.com/service-and-support/firmware-software/handheld-oscilloscopes/#shs800-series6) Plug the scope in via the USB port. It should grab the correct driver from the software installed above.
7) Run EasyScopeX and select your scope: Scope Tab \ Add Device Button \ USBTMC Tab
If you follow the above steps it's painless.
Couple of pitfalls that threw me:
1) There's another version of EasyScopeX on Siglents website which is older, but has a higher version number than the newer release. You need to pick the latest edition above with the lower release number, not the older version with the higher release number. The wrong version will not see the scope, even with NI-VISA installed.
2) The older EasyScopeX release comes with x32 and x64 bit signed drivers, but these are not recognised by Win7.
3) The document Siglent released above describing the driver installation procedure seems to be for the older EasyScopeX release as this distro comes with .inf drivers, but there's nothing in the document about this. It's a red herring if you're using NI-VISA. The newer EasyScopeX doesn't come with drivers as it relies on NI-VISA.