Since you need several actions to take place in sequence, you'll need to use Manage | Scripts to write a script.
Set Variable [$CustomerID ; Customer::CustomerID]
Go To Layout ["Confirmation" (Confirmation)]
Set Field [Confirmation::CustomerID ; $CustomerID]
Use the perform script option for your button to run the above script.
A simpler approach that does not even require a button would be to add a portal to Confirmation on your customer layout. If you enable "allow creation of records via this relationship", you can add records in the confirmation table simply by enter data in the bottom blank row of the portal.
Thanks for the help. Worked like a charm!