Can I dismiss someone who refuses to wear PPE?

Potentially, yes. If someone refuses to follow the health and safety measures that have been put in place to protect them, colleagues and possibly their customers, including (where appropriate) the use of PPE then this is a disciplinary issue and should be dealt with as such. Repeated failure to comply with the requirement to follow these measures, or a one off significant failure, may be sufficient to justify dismissal, depending on the circumstances.