According to
https://aws.amazon.com/snowball/pricing/, egress fees depends on the region, which can range from $0.03/GB (North America & parts of Europe) to $0.05/GB (parts of Asia and Africa).
So US$300K to US$500K for egress fees + cost of Snowball devices.
The major downside of Snowball in this export case is the size limit of 80TB per device - from https://aws.amazon.com/snowball/features/ :
"Snowball Edge Storage Optimized provides 80 TB of HDD capacity for block volumes and Amazon S3-compatible object storage, and 1 TB of SATA SSD for block volumes."
That'd be around 125 Snowball devices to get 10PB out.
If OP actually has 10PB on S3 currently, the OP may want to fallback to leaving the existing data on S3 and accessing new data in the new location.