Would it be too in-your-face or insulting if a small training session was conducted about this where everyone is invited?
No, it's just an information, and something the company wants to take care of.
Is there a better way to proceed with this?
The signs you put in the bathroom are commonly useless for the ones who know and already take care of their personal hygiene, and helpful (and not helpless, typo corrected thanks to @Brandin) for the ones who don't care and/or don't know.
In order to create awareness for the ones who don't know, it's always useful to show them the benefits of doing something. As a simple search (that you already did) can give many information (e.g. diseases spread not washing hands, I think you could let people know what they face.
Before you set up a meeting, you can send an email, sharing data about the diseases than can be spread. Or just say nothing, call for the meeting, and explain. But it's important that people understand that the company does that not to bother them or to "educate" them, but to protect everyone's health, including the company (less people calling off, better the rate of return, greater benefits for eveybody).
Then, when everybody knows, put the signs. As a nice reminder.
Don't put the blame on anyone, show them why it's good for them, AND everyone around them, and they will be more willing to listen to you. Create awareness for the ones who don't know.