My first comment would be one of simple mathematics.
You share a single common ancestor, your great-great-grandparent, their spouse (your other great grand parent) was unrelated to your DNA.
Your respective grandparents shared 50% of their DNA because of dilution by their spouses.
So then your respective parents shared 25% of their DNA because of dilution by their spouses.
That being the case, you and your 'cousin' each share 12.5% of your DNA being diluted by your 'other' parents
That being the case, if you and your 'cousin' had children they would share 6.25% of their DNA
With 6.25% of their DNA in common, your children wouldn't be much different that most of rural Europe, Asia and Africa
BTW, I have the above down cold because my wife and I are EXACTLY the same relations as you two are, my grandfather and hers were brothers