My worry - I won't fit.
It is not you that does not fit. It is the job that does not fit with you. Or, you and the organisation do not fit with each other. Organisational change is difficult and slow, and if you are a good fit for the position in other ways then you are wise to try to head this problem off at the pass.
You are probably not the only one who finds incessant body image talk distressing. What sort of pressure do you feel you will be under? To share my experience: I find diet talk difficult to deal with and typically look out of the window, say "hmm", or, if someone looks at me conspiratorially and mentions being "naughty" or "good", mumble vaguely that I prefer not to assign moral qualities to food.
As an admin do you have to interact with food directly, e.g. arranging catering for meetings?
I really do not think you are going to have to sit and eat your egg mayo sandwich in secret but if you choose to then why not? If you feel upset by the woman who comments on the calorific content of your food, you could look her in the eye and politely ask her not to do that, please, which might take courage the first time but would probably earn you respect in the long run. If her comments are leading to your self-esteem crumbling, then you could seek some support for that, here for example or from somewhere IRL - in a similar situation, I sometimes text or even go outside and call my siblings or friends.
Perhaps not in your first few weeks, but gently gently once you have your feet under your desk you could use your presence as a voice for change. I really do not think you will be the only person in the organisation who finds this tiresome. Botulin is a neurotoxin, and fasting is a choice, as is stomach waxing. These are personal issues to discuss in the work place and you are absolutely entitled to change the subject when they come up. As examples of what to talk about, maybe whatever people have in common, such as their hobbies or families, or current events - fashion, movies, soaps, Brexit, depending on the culture or industry. You could gently change the subject under the guise of getting to know your colleagues, or even just ask whatever constitutes a benign question about the job like do they have a party at Christmas or how to load paper in the photocopier, I don't know, whatever else you might think of. I would imagine that your colleagues have topics they could talk about other than body image concerns and that some of them will be grateful for the change of subject. Of course this is not your responsibility but it might help you to feel calmer if you know you have a strategy for when you feel distressed.
Good luck 