Although you cannot directly add a handling fee to your orders, what you can do is:

• Increase your product prices by X % — or add a flat amount — so that the handling fee is in fact included in your product prices OR
• Hide the handling fee in your shipping rates. In other words, charge more for shipping. Even with Carrier-calculated rates, you can add a percentage to all rates, so if you need to add a 6% handling fee, raise your shipping rates by 6%. The same way, if you need to charge a flat handling fee of, say, $8, then you can add $8 to all your carrier-calculated rates.