This does indeed seem like a great use case for a custom widget. I love the look of the wheel for selecting an item from a list. Your widget would likely operate on a Mendix enumeration or a reference set, such that the option you select from the wheel fills that value.
I would suggest to start with this article, which gives an overview of what you need- and how- to create a react native custom widget (called a “Pluggable Native Widget” – as opposed to “Pluggable Web Widget”) https://docs.mendix.com/howto/extensibility/build-native-widget
For any deeper questions about the native widget API, you can have a look here: https://docs.mendix.com/apidocs-mxsdk/apidocs/pluggable-widgets which is a nice overview to the types of settings that you can configure in your pluggable native widget.
I hope this helps you get started, and I look forward to seeing what you make!