He asked for my Skype?

Anonymous
I was chatting with a guy I met online for a few days now. I don't know him that well. I know just few basic information about him. Our conversations went pretty cool. Today, he asked for my Skype. I didn't feel like giving it to him, so I made excuses like "Oh I will Skype with you once I get new headphones because I like to Skype using headphones" I know it's a lame excuse, but seriously I like to Skype using headphones!
He told me they are other options available other than texting. You don't get to know the person that much through texting. He wants to see me through a video chat so that he could know me better, and see my facial expressions, smile, etc...
I then told him, it's too early to ask for my Skype. His response was "What if I'm dying in a few days! Will it still be early?" I don't know what to reply back. What should I say? Should give him my Skype even though I think it's too early? Or not?

He asked for my Skype?
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