Hi --- You can still take the item back and explain the problem, you don't lose your rights just because you've lost the receipt, however proving that you bought the goods there shifts the onus of proof onto you.
If you can reasonably provide other proof such as a credit card statement or other payment method, even the original bag, box or wrapping, maybe a witness who was present when purchased, possibly they will recognise that they supplied the goods as one of their unique brands or even take your word for it. !!
The best approach is just walk into their shop, ask to speak to a manager / supervisor and just calmly explain the truth, you may just find that they accept your word in this matter and offer you a straight forward exchange.