You can set timesheet requests for approval to the Delivery Manager and optionally always also include the Commercial Contact.
This is a system wide setting found in Tools & Settings > Resource Tools > Time & Expense Settings
This will ensure that the Delivery Contact and (where assigned in the Assignment record) the Commercial Contact automatically gets a copy of the timesheet approval emails ensuring a greater chance of a timely approval:
Whoever clicks 'approve' first once the email is received will be marked as the approver.