I will comment and respond as a phyician, oncologist, non-smoker and non-vegan. I would advise to quit smoking first given the fairly quick benefits of doing so and stopping the accumulation of risk associated with ongoing smoking as it pertains to cancers, heart disease and vascular disease. Having seen and cared for many, many smoking-related cancers, I can first hand tell you the devastating impact it can have. Of note I do have patients with cancers who have been Vegan for some time.
As a non-vegan/vegetarian, I will agree that a vegetarian diet is healthier - no question. But in comparison to smoking cessation, I feel that the transition to a vegetarian/vegan diet can be second to smoking cessation as "crash" dietary transitions are harder to maintain and I would advise that to make a healthier diet transition sustainable, one does so at a modest pace. Health benefits will come.
Now one disagreement I have with you is your apparent linking ALL animal products to the WHO statement - that is not accurate. WHO made a statement on processed meats (including cured meats). That did not include eggs and skinless chicken, both of which do have health benefits.
Thank you