I think you may be misinformed on how businesses report/pay sales taxes. For sales tax, depending on the type of business you are and your expected taxable sales, you may be required to report your taxable sales quarterly, biannually, or annually. Tax is due when the report is due much like income tax, but these cannot be delayed like income tax filings.
If you fail to make a report, the State will estimate your taxes and send you a bill. This bill will include late fees and charges. There is no incentive for business owners to delay these filings and payments. In fact, not filing and not paying may result in your sales and use tax certificate being revoked, effectively putting you out of business.
A business is also not required to set aside any certain amount from a single transaction and pay that to the State. They don't have to take $5 of your $100 transaction and put it in a "sales tax" envelope to send to the State. At the end of the period they have to calculate, $X in taxable sales * Y% tax rate = Total Tax bill, and pay that amount. They could pay it all from the last sale, or set aside a separate account, or a sub-account, etc.
So businesses don't have to pay immediately, they pay on a set schedule. The funds that they collect will most likely be deposited into a general account and the taxes paid out of that account at a later date. Yes, this may include revenue from the following month, but who cares? The point is that the tax is paid on time and in the amount required.
But to the question at hand... No, you cannot file a form or inform the business that you will pay tax directly. The business is required by law to collect those taxes at the time of the sale (unless you have a reseller certificate and they make those kinds of sales). They are not allowed to say "sure, take the X% off the price and pay the state, we trust you". They have to report taxable sales and pay the tax on those sales. Since your sale is "taxable", they are required to pay the tax on that, regardless of them collecting it from you or not.