Okay- first the safest way you can buy on eBay is with a credit card attached to Paypal (or one of the few similar services that eBay recognizes).
Not only is your cc number never shown to your seller, but if things go pear-shaped, you have a second tool for getting a refund through the card's chargeback service.
It is likely the card number is wanted by PP for any fees you may incur -- are you a seller as well as a buyer? Or you may not have enough in the particular account you want to use.
All sellers have to accept PP(or one of the few similar services that eBay recognizes). But some also have merchant accounts for their businesses, separate from their PP business.
That you are reluctant to send that number to an unknown seller is the reason that PP exists.
Generally, if a seller also has a merchant credit card account, he has been vetted by his bank, who don't want him skipping town with 'their' money. So you could be fairly confident in sending the number to him. We usually told our cc customers to email us with half the number first, then the second half , then the expiry and the number on the back of the card. Pain in the patootie, but ... trust.