Varric is about as magical as a... very not-magical thing. His crossbow Bianca is similarly non-magical, although it may have some form of runic enhancement to it- weapons in his world can be improved by attaching Tevinter runes inscribed in layers of folded lyrium, the magical metal. The closest the enchantments available through runes get to the Golden Sun elements is that he can have runes attached that add fire damage, cold damage, electricity damage, nature damage, spirit damage, or extra plain ol' physical damage. Bianca has two rune slots, so he could theoretically have two different types of extra damage installed.

Similarly, he can have armor runes integrated into his duster to protect him against various amounts of elemental damage. It won't make him immune, but it'll protect him against the worst of whatever-it-is. One option is a rune of lightning warding, so if it would help, I can say that he bought it and got it added at some point before coming to the Sol Sanctum.