Do not cancel the order. This is giving buyers an incentive to leave bad feedback and just sit back and wait for a refund. You did the work you get paid. Do not refund them.
Anything from this point on should not be about cancellations or refunds. It should be about resolving the issue but from what you posted above you made some mistakes here.
You should have been more specific in your language. First of all responding to a message that asks you if you can improve a product without any specifics is too vague and open to interpretation. your customer probably had their own idea of what improved meant and you had another. I would have responded with specifics,telling them exactly what you could improve so there was no confusion or room for misunderstanding.
I would not have responded to this 'can you improve my product?'
with ‘…Yes I can help you improve it’
this makes you sound like Yosser Hughes (Google it) and I would have been very specific about what you could or would do.
In my opinion this is exactly why the feedback and cancellation process was changed. Look at the people in here shouting “cancel, cancel” This is not going to resolve anything and will result in bad feelings on both sides. Maybe the buyer is up to no good, or maybe they had different expectations. Cancelling the order will just give them their money back and nothing else.
A lot of people on here seem to think the updated cancellation a review system is now skewed against sellers. I think you will find otherwise. Once buyers start to realize that cancellations no longer automatically remove feedback and refunds are not automatic & they can no longer alter feedback perceptions and attitudes are going to change and this refund mentality is going to disappear. I think you will find this is trying to force buyers and sellers to work to resolve issues instead of just cancelling orders and leaving both parties with a bad taste in their mouth.
Of course if a seller has provided something the dog dropped, instead of what the buyer ordered ,then its probably going to go to a cancellation and if there are bad sellers their cancellation rate will go up and their orders will go down.
likewise with bad buyers trying to take advantage of sellers. I think if you step back and take a look at how cancellations, reviews and refunds work that this will work against them.
With regards to this order. I would not cancel it. I would message the buyer and state I did x, y and z which is an improvement to the original product for the following reasons and see what they have to say.