As a developer who was in this same predicament myself, I highly recommend taking a look at the Human Interface Guidelines (HIG) for the platforms in question:
Those the respective HIGs for both platforms. Each platform has similar elements; however, they look very different. Also, both platforms have subtle variations in execution recommendations, which you should probably take into consideration. Taking these variations into account will be the only way to really make the experience feel native because, in theory, both platform owners will abide by the instructions in their respective HIGs when creating their own apps.
Most larger corporations will also have a Style Guide available describing how they, the corporation, would like you to represent them.
Unfortunately, I do not know enough about the particular implementation you are trying to achieve to say whether it can easily be accomplished using native UI components; however, I can say, that 99.9% of everything you see is done using some variation/combination of the native UI components with little (if any) actual custom drawing. You may have custom background images applied, colors, etc. - but mostly based on standard UI elements.
Having said all that, most engineers I've worked with are not very visual, as such it can be difficult for them to see how to break a design down into simpler pieces. So, if you can help them understand/see how to break it down, they should be able to handle the actual implementation relatively easily. (For example, while my app was on both platforms, I would actually do most of the XML layouts myself despite not knowing anything else about the platform.)
Hope that helps.