Items are supposed to be returned in the same condition they were sent. However, since the final decision would be either Paypal or his credit card chargeback, who cannot see the shoes, this is moot.
Did he leave feedback already? If so, you can refuse the return, safely, since he cannot directly harm your reputation. If he did not, he has a powerful weapon in the Detailed Seller Ratings, which are much much more important than feedback. If your DSRs drop below 4.3 there will be restrictions on your selling activities. This is very important.
If he has not left feedback, tell him to return the shoes with Delivery Confirmation. From the USA this will run him $20-$25 or more, but is required if the problem goes to a Paypal Dispute. The cost of return may discourage him.
You can Respond to any feedback (including your own). Responses should be calm and factual for best effect, but are not required to be positive.
Do not refund without return. Do not offer a partial refund. Not only will neither of these help with your feedback/DSRs, in the long run they will hurt every seller he deals with in future.
And “lose” what? If he does return them and you refund him, you are out the postage costs and the difference between your selling price and your purchase costs (including eBay fees.). You may be able to sell the used shoes for your original purchase cost. Maybe.
