I had an old Suzuki 750 triple 2 stroke that had a fan on the rad. Not much different in loc and size to our oil cooler not sure how much it would benefit you but it is doable. Air flowing across the fins on the jugs and head is where most of the cooling is.

Actually still have the old 750 out in the shed buried under junk. Ran when I put it there.

I learned all I need to know about life by killing smart people and eating their brains.
Eat right ,Exercise ,Stay fit, Die Anyway!