This feature is now available in vivaldi 3.4 from the profile manager menu - make sure to not delete the image file you choose from disk. I suggest moving it to your profile folder first. https://vivaldi.com/blog/vivaldi-3-4-desktop/
Having come across the situation where I now occasionally need to use multiple machines in a networked windows environment I have renewed interest in this request.
Specifically, to split up the useful information (settings, bookmarks, extensions) from the useless fluff (gigabytes of cache).
I suspect due to the whole thing chrome does about encrypting settings by user on Windows and so on this would be very difficult to get working across machines.