If you really need to write it manually, then you should have access to an implicit props that contains a reference to the ComponentStore, which itself contains a reference to the component's props, meta, custom as PropertyTree objects with a write method, e.g:
this.props.store.props.write("path", value);
However, the input fields in Perspective are a fair bit more complicated than just simple <Input> wrappers since they need to handle theming across browsers, the "defer updates" settings, and some other aspects. It may or may not be easier to extend the base <InputField> class for your own purposes.