For financial institution reporting to you, yes, blank is a valid choice. Your financial institution doesn't have the date you purchased the stock. However, you, as the taxpayer, needs to enter a date that you acquired the stock. The IRS needs a date so they can determine how they're going to tax you. A short term stock sale is taxed differently than a long term stock sale.
Try to narrow the purchase date down to a date or a date range. Document how you came up with a date. Once you have that, follow these instructions to locate historical prices.