First, save all emails and other evidence. Second, I am not going to say you definitely can do that as there are more details a lawyer would want to know. But in general, if the other side of a deal repudiates it, then you do not have to go through with it. I see some problems. They only said they were thinking about disputing payment not the they definitely would, so there are questions to be resolved. The risk is they will buy a cooker somewhere else for more money and sue you for the difference in price or something like that. Best bet is to try and work things out with them. Next best is to talk to a lawyer in person.
This is not legal advice. You should always discuss the specifics of your issue in person with an attorney. Be aware that there are time limits on all claims that depend on the kind of claim, so do not delay in seeking an attorney.
Your question is a surprisingly difficult one. The answer will depend on many different factors. I would like to point out a few potential issues I see. Of course, none of these will be an issue if the buyer agrees to accept the refund and drop the issue.
1. Did your contract give you the right to do what you are thinking of doing? If so, you probably do have the right to do it. If not, your situation could turn into a knock-down-drag-out legal battle.
2. I agree with Mr. Arbuckle that a party to a contract may breach the contract in anticipation of the other party's breach. This is called "anticipatory repudiation." In your situation, there will be some questions about whether the email was enough to justify your anticipatory repudiation of the contract.
3. I would also like to add that if you knew why the buyer needed the cooker, you might also be on the hook for "consequential damages," i.e. losses he suffered as a result of the breach such as money buyer missed out on because he did not get the cooker on time (not just the difference in price between your cooker and a more expensive replacement). (Section 2.715 of the Texas Business and Commerce Code).
4. You said it was not your fault that the truck broke down, but you probably had the risk of loss while the item was in transit. ( Section 2.509 of the Texas Business and Commerce Code).
Please feel free to contact me if you wish to discuss this matter further.
You have a typical business legal problem. It is not unusual but it is fact intensive. That means that the best course of action for you will depend upon a clear understanding of all the facts by a lawyer who is familiar with the law applicable to this subject. This website is not intended to provide specific legal advice. It can only provide generalized information. You need much more than that and you need it quickly. You are in a business. You need a relationship with a business lawyer so that when things like this come up, you have someone to go to who understands your business. This would be an excellent opportunity to establish that kind of relationship with a lawyer in your area.
DISCLAIMER: This is not specific legal advice and does not establish an attorney/client relationship.
I agree with the excellent answers you have received from Messrs. Arbuckle, Scott and Paxton.
Because this is more of a commercial law question than a "lawsuits and disputes" question, I have edited the practice area you specified accordingly.