Is this agent representing both the buyer and you? If so, they can provide the Listing Agreement that they signed with the Seller. That is not the same as the MLS Listing. These are two separate entities, at least in Florida.
As part of your contract, do you have an addendum that states the seller gives you the right to market for sale, negotiate, and enter into contract to sell immediately? If not, then you should probably add that to your contract, unless prohibited by state law.
Another addendum you can add is that the homeowner agrees to have their realtor remove the listing from the MLS once you have a signed contract. Again, this is only valid if it does not violate state law. If legal, then per these two addendums, you would have the rights to have it posted on the MLS through your realtor and he can market it just like any other property.
One caveat to that is that there are some realtor regulations in each state that might preclude the marketing on the MLS without stating that there needs to be third party approval, which can then cause other realtors to not bother showing the property.
Your realtor should also be posting this property on Craigslist, Kijiji, and other sites, if they are an aggressive realtor.
You should be able to market to both cash and financed buyers. There are ways to market this that do not require listing on the MLS and as long as you fully disclose to the end buyer AND HIS LENDER what you are doing, then you would normally not have a problem (unless it is an FHA loan).
I put that last in there, as it is still unclear whether they will require your name to be on the deed before they will underwrite the policy, which means they will not underwrite until after you have closed and the public records have been update.