Are Bluetooth earbuds really safe ?

Show him you using them without harm. You  haven't talked to him enough throughout his life. Teach him carefully that some people are asssholes who like to lie to others to make them feel bad.

I'm smarter than these fools so here is what I would do.

I would teach him about resistance. He doesn't need to understand the details, but he should be able to understand that those earbuds do NOT have enough voltage or amperage to shock him. 

I would open up the hood of my car, show him the battery, say "This battery has 12 volts and 600 amps worth of power. It is strong enough to start this entire car. And THEN i would literally touch my fingers to both the positive and negative sides of the battery. It will not shock you at all. And then I would be like "Do you know why I'm not getting electrocuted right now? Because human bodies have resistance to electrical shocks. Dry hands have about 40,000 ohms of resistance. Anything less than 12 volt electricity cannot hurt you. 

120 volt AC from a wall can kill you but 12 volt DC cannot hurt you. You can feel about 12 volts on your tongue because your tongue is wet and therefore more conductive, but with dry skin you're not going to get shocked.

Those earphones probably operate on like 6 volts and like .1 watts of power They will never harm him in any serious way. As long as he doesn't choke to death on them, he is completely safe while using them.

5volts or less is considered inherently safe.  5V is the standard for electronic devices now.

Send the pic are they wireless?? 

I can’t judge like that 

Perfectly safe. They don't hold enough charge to hurt a mouse and they're covered with plastic anyways.There's more worries about running out of charge than it hurting you.

They are absolutely safe. If the urban legends about electrocution were true--if people were even receiving mild shocks from them--they'd be in the news, there would be individual and class action lawsuits, there'd be a massive recall, and they would not be in stores.

This is a great parenting opportunity to teach him how to identify trusted sources of information.