Ah this old chestnut!
I've had to have this conversation with three employees in the past. But all worked for me. So in my mind, that was my job. HR should not automatically be sending it to the QA team but with how the HR function has changed in the last 20-30 years, you need to face facts, they will be sending it to the line manager to sort and won't be doing it themselves. But that's a commentary on how HR has been devalued and everything has been piled upon overworked line managers and a different topic altogether.
On how to approach the conversation, the last one I did went better than the first. I gently but genuinely said to him "you are a talented employee and I don't want something like this to hold you back."
I meant every word, he took it as it was meant and changed his washing behaviours.
But sensitivity is required and I'm sorry, this really still does not mean HR are getting off their a**es to help you. They honestly are down to 1-2 people for hundreds or even thousands in most factories I've worked in nowadays. As a manager, you should know the law that applies in your country for equity and diversity and be able to have difficult conversations. So yes, be sensitive. Consider that there may be medical conditions or home situations which could be impacting their ability to stay clean and hygienic. Offer help. In the UK there is a charity called "Grocery Aid" which anyone in the food industry can access. They can award grants to people on hard times and might be able to help in this situation if the problem is an insecure housing situation or a mental health issue which means the person is taking less care of themselves. I'm unsure if there is similar in the US or other countries.
And lastly, if HR have batted one to you that isn't from your department, point out they should be talking to the employee's line manager. It ain't your job in that situation.