I think that will depend on how you're pulling/storing the delivery date into your database and how you want to display it. I would start with web/OPCControls/ShippingMethodSelector.ascx, the shipping display starts around line #17.
<asp:RadioButtonList runat="server" ID="ShippingMethods" AutoPostBack="true" OnSelectedIndexChanged="ShippingMethods_SelectedIndexChanged" />
You'll need to get into the codebehind to pull in your new value. It might be tricky to display a date per shipping method, looks like it should be doable without full SOPC source though.