Of course, if the contract is already done and submitted, and the buyer is paying cash for the furniture, then it's really not that difficult, just do the contract and call it a day, just don't submit it with the other paperwork. It's technically none of their business. And again, unless you're actually making money off the furniture, no tax implications.
Just to cover my butt on this, check with an accountant, but I'm pretty sure I'm right on the tax part....
In the event of personal property and trade fixture in the sale of a business, those, at least in California, require reporting to the Sales and Use Tax Board, fees paid, and a Bulk Transfer Notice for the Business. But it doesn't appear this is your question.
All the best to you.