In Windows 8.1, there was plenty of documentation on what registry keys to modify in order to hide OneDrive from explorer, see for example here. Unfortunately, the class ID for OneDrive changed in Windows 10 -- use the following registry location instead:
HKEY_CLASSES_ROOT\CLSID\{018D5C66-4533-4307-9B53-224DE2ED1FE6}\ShellFolder
As described in the original EightForums article, set the "Attributes" key to f090004d. I've also discovered that in Windows 10 it is not necessary to perform the "64-bit" actions (no similar key exists under the Wow6432Node).
That already visually removes OneDrive. Next up, make sure it doesn't start again by modifying the "OneDrive" application settings. As back in the pre-Windows 8.1 era, OneDrive can again be disabled by rightclicking the OneDrive icon in the notification area, going to settings and disabling...
Finally, don't forget to enable "Save to Computer by default" in the various Office applications to prevent Office of trying to find that OneDrive folder again...
Et voila, at least in this Technical Preview OneDrive can be circumvented this way. No guarantees whether this will still be the case in future TP's or the RTM version of Windows 10 though...
Please note that this does have an impact on functionality, as Microsoft still has big plans to use OneDrive as to share data & settings across the entire Windows 10 platform - read Paul Thurrott's view on it here.