Actually you can disclose pending offers with the sellers permission. Generally sellers on short sales don't care as they get no money from the sale. Occasionally if it is an FHA loan on the short sale they will get 1,000 to 1,500 dollars to help relocate.
If you the buyer just submitted an offer and want an approval in 10 days you are dreaming or smoking the good stuff. Now if a BPO or Appraisal depending on loan type has been completed and all sellers requested financials are in then getting an answer faster is possible.
There are so many factors like which company is servicing the loan or loans,how many loans the property has,extra liens on the property (judgements,tax liens,mechanics liens etc.),and which banks own the loan or loans.
Good luck. With the individual complexities of each short sale it is impossible to answer your question on here.