This is an interesting question.
I would hazard against using a dropdown. In general, they're frowned upon for mobile UX because they require a "tap" to view the options, and another to select one.
Segmented Controls: Maybe
Normally, this is where I would point you. It might still be an option, depending on your data. Instead of going the traditional route of "Button Groups", it may be worth creating a new component that fits your data better.
New Componenet: Yes
This likely has a name, but why not something like this?:
(I did this in paint. Open to suggestions for a better program).
Where you use some kind of list component where the entire area is tappable/clickable. Just make sure the element has a "selected" state. It's definitely more work, but I think it's a huge improvement for UX.
- More aesthetically pleasing.
- Larger hit area.
- Accommodates longer strings.