The only significance of $10,000 is that it’s the amount that triggers reporting. Such transactions aren’t illegal or even suspicious. They’ll write you a check

The only significance of $10,000 is that it’s the amount that triggers reporting. Such transactions aren’t illegal or even suspicious. They’ll write you a check for the full amount and the other bank will accept it. There might be a hold on the funds for several days until the check clears. As another commenter mentions, you can open the new account first and do an electronic transfer which will make the funds available sooner.