For your non-shippable deposit product, just leave Shipping/Buyer's Address disabled in the product's settings.
For your 4-bottle product, your $5 per-order Handling charge would still apply, so you just need to make up the remaining $15 difference. Go to Seller Admin > Cart Shipping Settings, pick a Packaging Type you don't use for any other products, and set that package's Cost to 15.00. Click Next to save that setting, then click Back to Admin.
When you add/edit the 4-bottle product, be sure to enable Shipping/Buyer's Address in that product's settings, then click Next to reach the product's Shipping Options screen, select the same Package Type that you'd configured with the 15.00 Cost setting, then click Next until you can Submit changes.