Are there any showers international transit passengers can use at Guangzhou airport?

I am sorry that there is no such kind of service in the airport, but there is a hotel in the airport. You can book a room in it for several hours to have a shower in it.
You can use your credit card in the hotel.
As for the price, it is difficult to tell you, because I did not live in it just for a shower. You can ask them directly and I think they will give you a suitable price.