Arrival at Guangzhou Baiyun Airport after 1am, what is the cheapest & safest way to go to Hong Kong?

I'm afraid there is no way to your demand. It is suggested to stay in GZ for a night. In the next day, you can go to GZ East Railway Station to take a direct train to HK within around 2h.

Upon your rrival at 1:00am, shuttle bus line 1 and line 6 would still be in operation. By taking either of them, you can go to GZ city center.