While highly sensitive data like personal health information (PHI) is valuable to digital health service providers, users often remain reluctant to disclose such personal data. Research has shown that personalised nudging, i.e. nudging that adopts content to user characteristics to nudge specific actions, can successfully increase purchase intention. However, its effect on consumers' handling of sensitive data is unclear. We apply personalised nudging in the context of personalising data usage policies and investigate whether personalised nudges that match users' cognitive styles (i.e. the way users process information), affects individuals' level of trust, privacy concerns, risk, and PHI disclosure. Using an online experiment in the context of mobile apps for health bonus programmes, we find that, when presentation format matches the users' cognitive style individuals' PHI disclosure and trust are not affected, but that individuals' privacy concerns and risk perceptions are significantly lower.