To do this you'll have to either locate existing dataproviders for this, or write your own dataproviders.

Personally, I would never advise a client down such a path, using the MSSQL allows you so much more in terms of options for modules and future upgrades.

If you're looking to just use your own DP in your own modules there are a few different ways you could go about building those. You can simply include a connection string in your web.config, hard coded into the module, or even stored in the module settings, to make your module connect to whatever database you want. It doesn't necessarily even have to follow the dataprovider model.

The provider for DNN is in the Source version, should be it's own project file in the solution.