When I grew pawpaw trees from seed, The seed went directly into soil without any refrigerator involved.
I'd get those planted... My reading suggested that dry seeds were dead.
I tried refrigerating buckeyes once... Because they come up immediately when planted...
Unfortunately, that didn't work... they were all consumed by worms.
So for buckeyes, I keep inside after planting... Seems like I did the same with the pawpaws.