You still have to refund. Any insurances is for your protection as the sender of the goods. After all, the contract is between you and the post office, and if goods you posted don't arrive, it is up to you to chase the compensation from the post office.
If you choose to gamble by sending goods valued at over �34 without extra insurance, then that is your fault. 'Signed for' does not provide extra insurance, or any different insurance to the standard first or second class post - it simply proves that somebody has signed for receipt of it.
Under English law, if you accept money for goods you must supply the goods. Your responsibility does not end when the post office takes the parcel.
Your buyer could take you to Small Claims Court for a full refund - and if you can't prove he received it, he will win.
I have helped many people get their money back through the Small Claims Court in this scenario - all from private sellers, not businesses, where the sale has not been through PayPal. Where PayPal has been used, the refund is automatic when the seller cannot prove RECEIPT of goods, not postage of goods, as you probably know.