I've just made a very ugly, but perfectly working workaround for this WITH PURE CSS (no JS needed).
I came across a CSS stylesheet full of 'vw' declarations (also for heights and top/bottom properties) that needed to be rewritten for native Android Browser (which in versions 4.3 and below does NOT support 'vw' units).
Instead of rewriting everything to percentages, that are relative to parent's width (so the deeper in DOM, the most complicated calculations), which would give me a headache even before I would reach the first { height: Xvw } declaration, I generated myself the following stylesheet:
http://splendige.pl/vw2rem.css
I guess you're all familiar with 'em' units (if not: http://www.w3schools.com/cssref/css_units.asp). After some testing I discovered that old Android Browsers (as well as all the others) perfectly support the 'rem' units, which work the same as 'em', but are relative to the ROOT element font-size declaration (in most cases, the html tag).
So the easiest way to make this work was to declare the font-size for html tag that is equal to 1% of the viewport's width, e.g. 19.2px for 1920px viewport and use a lot of media queries for the whole 1920-320px range. This way I made the 'rem' unit equal to 'vw' in all resolutions (step is 10px, but you can even try declaring html{font-size} for every 1px). Then I just batch-replaced 'vw' with 'rem' and admired the working layout on Android 4.3 native browser.
Whatsmore, you can then redeclare the font-size even for the whole body tag (in whatever units you want: px, em, pt, etc.) and it does NOT affect the 'rem' equality to 'vw' in the whole stylesheet.
Hope this helps. I know it looks kinda silly, but works like a charm. Remember: if something looks stupid, but works, it is not stupid :)