Ask your realtor to write it up and if they are reticent, tell them you'll get another realtor who will. Ask them to do a market analysis and make a fair offer on the property. Since there are other offers you'll want to be competitive, but if they let slip that there aren't other cash offers then you might have a chance.
If your realtor is not full time and is shy about short sales you probly have the wrong person (no offense). Short sales are such a big part of the landscape now that if you're a realtor and haven't taken the time to become comfortable with the process of short sales, REO's and foreclosures, then you should look for another profession. Again, no offense....but if you can't be one of the best, why play? If you are a buyer you should trust your realtor and have some confidence in them that they know what they're doing and that they're looking out for you. I'm just sayin......
The big question is if the seller has signed an offer. The seller can only sign one offer. Find that out...if the answer is no, then you can/should submit an offer. If the answer is yes, then you can only be a back-up to the first offer, which is probably a big waste of time, especially for a short sale. As for being cash, it is probably no difference to the seller's bank....it is all a bottom line loss to them and what they are willing to do vs seller's foreclosure / hardship. You also won't be able to close asap, because you'll be at the mercy of the seller's lender, which usually will take 60-120 days.
If the bank hasn't made a decision and the sellers are willing to take another offer, then you should be able to submit the offer (the sellers are not obligated to look at any more offers). With 2 other offers on the table, your offer would have to be pretty strong, although paying cash is always a plus for sellers and the banks. I understand your agent not wanting to get involved in a short sale, but he/she should submit an offer on your behalf if that is really what you want to do.
Good luck to you!