The 1099-Q must only be entered if it is greater than the eligible expenses. If all of the $10,000 went towards eligible expenses, tuck the form in your folder.
You are correct that you can't double dip and claim medical expenses with some of the money. Your method sounds logical but is not quite right. See the first reference below for calculation and examples.
If you are claiming that not all of it went toward qualified expenses, then you will need to enter it and eligible expenses.
Reference:
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