Can you please confirm the exact Data Transfer OUT cost when exporting data from Amazon S3 to an AWS Snowball device in the Mumbai (ap-south-1) region?

When exporting data from Amazon S3 to an AWS Snowball device, there is no data transfer OUT charge for this specific operation. According to the AWS Snowball pricing information, data transfer IN to Amazon S3 is $0.00 per GB (with some exceptions for small files), and while data transfer OUT of Amazon S3 is priced by region, this refers to data transfer to destinations other than Snowball devices.

When using Snowball for data export from S3, you pay for the Snowball device usage (which includes a service fee and potentially additional per-day fees if you keep the device beyond the initial period), but you don't pay the standard S3 egress rates that would apply when transferring data to the internet.

The standard S3 egress rates you mentioned ($0.109/GB for first 10 TB, $0.085/GB for next 40 TB in ap-south-1) would apply to data transfers from S3 to the internet, but not to transfers from S3 to a Snowball device.

Note that you would still incur Amazon S3 charges for the GET requests needed to retrieve your data from S3 during the export job, but not for the actual data transfer volume itself.
Sources
AWS Snowball Cost - AWS