Karo substitution for the syrup mixture? Can I just heat it up?

I wouldn't do that, because Italian buttercream is tricky enough as it is, without introducing a variable that hasn't been tested with (or if it has been, has not been incorporated into) this recipe.

Instead, I'd look for a recipe that was developed with corn syrup in mind, such as this one: https://www.finecooking.com/recipe/buttercream-frosting
I was interested to read that the authors of the article on this site in which buttercreams are discussed state that they like using corn syrup because you don't need to monitor the temperature with a thermometer. https://www.finecooking.com/recipe/a-guide-to-buttercream-frostings
;o)