It may have been his wish, but I am not surprised you are feeling lost and empty. There is so much loss around a sudden bereavement, all the thoughts of the future experiences you can never have and so on. I am sorry to say that I have no easy solutions and can only suggest taking your time. 

Pethaps in time you can build a connection with his wife, if you wish. You are certainly able to purchase his death certificate (anyone can buy anyone's) which would give you some basic information if there is no other way to find out and it continues to be important to you.

Take care of yourself. x 

You also say that he died a month ago on 1st November. It's only been just over two weeks. It is likely that he was only cremated in the last few days and the flowers would still be at the crematorium. One option is to take a drive around a few and have a look, our local crematoria leave the flowers for a week. This might bring you some closure and enable you to find a focus for your grief. 

Some people turn into vultures after a death. It may actually not have been his wish for you not to know. He may have wanted belongings / money left to you and this is her way of keeping you away in the dark. Possibly speak to a solicitor?