You can use the CBSubs Promotions engine and Tax plugins for that with an automatic conditional "promotion":

Just create a non-coupon promotion with your shipping price (fixed, percent, fixed + percent, or depending on itme cost etc, see Promotions chapter in CBSubs manual for the extended possibilities) entered as a negative discount, and name your promo "Shipping costs".
Then in geographic conditions, select the geographic zone defined in the Taxes plugin to apply the promotion only to exports.

Alternatively you could probably create a negative fixed tax for exports only as well.

Using priorities and proper ordering of taxes you can then apply the real tax on the shipping costs too.

Hope that solves the conditional shipping costs

The Promotions engine is very flexible and allows many more use cases.