How do I ask Japanese restaurants in writing not to serve me any meat?

Please do not use Google Translate for Japanese without native speaker proofreading. The example sentences you provided are somewhere between comical and borderline offensive and sound rather like a mother scolding an unruly child (or husband).

justhungry.com (no affiliation) has a nice series of Japan dining cards that convey various dietary restrictions respectfully. Here's the one you probably want:

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I cannot eat any meat including chicken. Fish is ok. Thank you for understanding.

Also, if you're hoping for vegetarian omakase/kaiseki, you really should let them know well in advance at time of booking, instead of expecting them to be able to improvise.

lambshaanxy's card is perfectly fine, but I would like to bring up a cultural point when asking for accommodations for your meal.

Japanese restaurants are not accustomed to altering menu items to customers' preferences. In America, you can ask McDonalds to hold the pickles on your burger, but this kind of request in Japan will often result in the employee getting permission from the manager. The same is true at any level of restaurant from street food to Michelin star. Japanese food culture focuses heavily on preparing dishes to a very specific formula that the kitchen staff often spend years perfecting. Asking them to change your dish would be like asking a classical painter to do a caricature, or a Philharmonic orchestra to play Kidz Bop.

Instead of asking for them to remove meat from a dish, ask for dishes that do not contain meat. Say something like: For health reasons, I cannot eat meat or chicken, but fish is okay. Can you recommend any dishes that meet these requirements? Thank you for understanding.

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I studied Japanese for a couple of years (ahem, a while ago). I think you may be better off with simpler statements. Asking if they can guarantee that you won't be served meat seems strongly worded to me for a Japanese context.

I looked at a few sites like this one to get some ideas.

You're much more likely to be served something with seafood in it rather than with meat (although watch out for bacon, I guess). Dashi, bonito flakes, roe (fish eggs) all get used in a lot of sauces and dishes where you might not expect them.

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Sumimasen. Niku ga taberaremasen.

Excuse me/sorry. I can't eat meat.

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Sakana wa daijobu desu.

Seafood is fine.

When you're actually ordering, check whether there's meat by pointing to the item and saying:

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Kore wa niku ga haittemasu ka?

Is there meat in this?

Hopefully, the server will answer something like:

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Niku ga haittemasen.

There isn't meat.

If you want a stronger statement:

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Oishasan ni nikurui o tabete wa ikenai to iwa remashita.

My doctor said that I can't eat meat.

A recent news show that I was watching noted that some restaurants are now asking customers who ask for allergen free items to sign an allergen waiver, noting that removal of all allergens is impossible and that they can’t take legal/medical responsibility if you have a reaction.

Some of the translation cards I’ve seen are worded in such dire terms (anaphylaxis, etc) that a restaurant may ask you to leave rather than serving you because they do not want to risk a claim of cross-contamination. So I would find a translation card that matches your level of sensitivity and be aware that people with food allergies are not a protected group in Japan.

I make this an answer, although it is not about the language but more about the culture. While there is a concept of vegetarianism in Buddhism in Japan (and you can get delicious vegetarian food at a temple which provides meals), and there are a few vegetarian restaurant (need to research them before going) outside of that it doesnt seem to exist. It is not uncommon to have even rice sprinkled with shaved meat. I went to a large international Conference in Japan and the conference served meals, so they knew that some people do not eat meat, so they provided toast with pumpkin as a replacement for every single meal.

It seems like having a little bit of meat in a dish is considered a nice gesture.

So my recommendation would be look before travelling for vegetarian/vegan restaurants, and do not expect to get food made without meat (if it happens, this is great of course)

Reusing lambshaanxy's answer, I added a second paragraph asking politely to either remove the meat or serve a fish-based dish instead if possible.

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It will work better in small non-busy family-owned restaurants, and ryotei if you show this when making the reservation. Chain restaurants, and places that serve only a small selection of dishes, might not be able to serve you.

Beware that a lot of soups have some amount of meat inside, but staff might not consider them as meat dishes.