You cannot do anything until the divorce is finalized. If you have a divorce attorney, they should draft your special warranty deed pursuant to the terms of the divorce decree. If you do not have a divorce attorney, you really should go to see a real estate attorney to draft the special warranty deed for you. These are not generic forms and require special handling to make sure the conveyance complies with the divorce decree. An owelty is just a lien and note specified in a special warranty deed if one party is awarded the property, but the other party does not receive enough other marital assets to match the value of the awarded property. A quitclaim deed does not convey title, it only releases a claim to title (which is a different thing), thus will not transfer the property. Good thing for you is that you will probably not have to refinance the mortgage because your husband is not on the promissory note. Again, you really need to go see a real estate attorney to assist you with this.
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Do not use a quit claim deed. The easiest thing is to go to your divorce attorney and have him or her prepare a deed to convey your ex's undivided interest to you. Expect to pay from $100 + for the document preparation and it should cost about $20 to record in the office of the county clerk.