Sorry for the loss of your cat. 13 years is a long time. I've had my cat Sphinx for 14 and tomorrow I have her booked for euthanasia.
I think that you should do what your instinct tells you. Burials and cremations are more for the living than the dead. I've kept the ashes of my cats with me in an urn, I feel comfort in having them near me at home. I understand what you mean with thinking about the decomposing or burning, I did that too but I had to shut the thought down, it was unbearable. Just remember that they aren't in the body in anymore but rather in spirit, if that helps. I don't really believe in afterlife, but for the last little while I've had two signs that my oldest cat and soulmate, Beck, has been looking over me during this difficult time. I think you know the answer to your question and you should go with what you feel is right and will make you feel better. Take care of yourself.
“Until one has loved an animal, a part of ones soul remains unawakened” ~ Anatole France