If you want to sell then you will have to supply bank details, so you have a simple choice, sell or not sell.
This is not just you, it will involve millions of sellers,and most will carry on as usual. Paypal will still be one of the methods of payment, but you will need to arrange to fund the payments.
Why should you be reluctant, you supply your bank details to Paypal if you withdraw money, you give card detail if you do any shopping online, and every direct debit or standing order you set up, and all details are on any cheques you write.
Why do you think you are at any risk giving details to ebay?
