No, you need to set it on the order data being sent to Klarna.
In KlarnaPaymentConfigV3.UpdateDataSentToKlarna you can access the .Tags property on the CheckoutOrder object to pass along parameters directly.
About tags at Klarna: Klarna API Reference
On the CheckoutOrder.OrderLines collection there’s also a property ShippingAttributes that has Weight and Dimensions, which I think you should use in your case. I haven’t tested this scenario myself.
About attributes at Klarna: Klarna API Reference