This is a slightly older thread, but you should have a finalized trade offer at the very least days before your delivery date. Since trade quotes are valid for 30 days, wait until you are within a week or so of your delivery date, make sure your trade quote isn't about to expire immediately, and get a check from your credit union then. That could even be drawn up the day before or day of delivery if required.
You shouldn't only be receiving your trade evaluation day of, meaning you'll certainly have that time in between the two to get the check. Also, ~48 hours before your delivery time you should receive (at least in Canada) a document outlining the exact financial terms of the transaction including sales tax, less the trade quote, etc. That document is what you would provide to your credit union to get the exact amount in a wire/draft/check to pay on day of. You may also need that document to obtain license plates/registration for the new vehicle too, as proof of purchase and sales taxes paid.
