First of all you won't be able to change anything into broker db via API and I would recommend not to do it either. The only way changes should go into broker db is via publish.
Having said that, for client side cache busting you can implement something like the below:
When any css file is added to cms or a reference is added in content, you can use datetime stamp as the version for the fully qualified url as a query string param. This can be easily done using event system. Alternatively if you refer CSS from an external system and just have references, you can write a tbb to add datetime of modified time of the page/component as the cache buster.
We use option 2 and have been using it without issues.