Buyer financing contingency about to expire and no appraisal has been done

I am a short seller of a home under contract with a buyer who is seeking financing. We have the third party short sale approval from the bank. The 30 day financing commitment letter contingency expires June 4, 2012. The appraisal has not been ordered yet. The buyer's loan officer keeps telling my realtor that everything is going fine and he sees no reason why it would not close. However, we feel we need that commitment letter on time and would prefer that it did not have a condition such as "subject to satisfactory appraisal." To us, that would mean nothing more than a fancy pre-approval letter. We do have a cash back up offer at the bank's approved price. Is it possible with the short week ahead to get an appraisal done and back and then a financing commitment letter for the buyer on time by the 4th? Would the file even be reviewed by an underwriter without an appraisal? It's conventional financing with seller (bank) paid closing costs. So, the cash back up offer is more money for the bank. Should we offer our current buyer an extension addendum, or move on to our cash back up offer? We would hate to move out, not close with the first buyer and have an abandoned home. We would also hate it if we waited to long and our cash back up buyer moved on. Our short sale approval letter expires 6/22/2012. Would love some feedback. Thank you.