Surcharge for certain items shipped Internationally

Good Morning all.

I am looking for some guidance on how to set up a surcharge for shipping specific items internationally.

Our shipping module is the Flat Rate shipping, duplicated to allow rates for Air, Ground, International, Canada and US. This works perfectly, except for a few select items.

We have about a dozen items that we need to charge a set handling fee for in order to ship them internationally, due to the unusual dimensions. But only those dozen or so items, all other items have our normal rates.

Is it possible to set up something like a handling fee for these items?
Or a special shipping module for just those items when shipped Internationally?

I have spent some time searching for an answer, and maybe I found it but am too sick to understand it, not sure. Help and guidance are appreciated.

Thanks

Myles

Some more clarity, if it helps.

Set a fee for just certain items and ONLY if those items are shipped internationally.

And that fee is not cumulative if combined with multiple items of the same type (can ship several in same box).