In Seller Admin > Cart Shipping Settings, pick a Package Type that you aren't using for any other products, and set its Cost to 4.35 (since you're already charging a 1.00 Handling fee on every order), click Next, then Back to Admin.
In the settings of each product that will ship at this flat rate, set the product Weight to 0.00 (this should exempt these products from your usual USPS/UPS rate lookups), select the same Package Type you'd assigned that Cost to, and specify a Capacity for how many units of that product will fit in that Package (i.e., how many units of the product can ship at that 5.35 flat rate).
