If you refuse that contingency, I would take my offer off the table. I understand why you wouldn't want that as a seller, but no buyer or competent buyer's agent would submit to those terms in this lending environment unless they were stealing the house from you.
Typically if the house doesn't appraise for the agreed upon price or more you would have the options of seeking another appraisal to meet that price, lowering the price to the appraised amount or the buyer would need to have sufficient cash to make up the difference as the bank won't consider it.
Appraisals are out of the agent's hands these days. We can no longer call on our local appraiser and threaten them with the loss of our business if they don't come in at value or better. Appraisers are supposed to be independent and non-partisan to the buyer, seller or lender. The current system has flaws, but it works for now.