So, he’s been a perfect tenant of yours for 11 years and now your trying to find a way to get his estate to pay for your refurbishment by using the excuse that he was a smoker and unclean? If you were not happy with him you should have taken action against him within those 11 years prior to his death. Regardless of his death, after 11+ years you should be refurbishing the property anyway.
I find what your doing very unethical and gives us landlords a bad name. At the most keep his deposit, return his over payments, cancel the standing order and refurbish at your own expense. Do not involve yourself anymore with his estate/family (its none of your business), move on and get new tenants, rather than trying to take advantage of his death.