No cancellations for rain, only cancellations for storms.
The event will be cancelled if there is stormy weather, but the event will proceed as planned even if it rains.
The event will not be cancelled for rain, but will be cancelled if the weather is stormy.
1)"No cancellations for rain, only cancellations for storms."このような略された言い方はよく看板などに書かれています。少し曖昧なので、看板以外は1)か2)のもっと長い文を使った方が明瞭です。
2)"The event will be cancelled if there is stormy weather, but the event will proceed as planned even if it rains."ちょっと長いですが、誤解されないように慎重な説明が必要です。
3)"The event will not be cancelled for rain, but will be cancelled if the weather is stormy."これは2)と同じ意味ですが、順番が異なります。
ところで、"storms"は幅広い言葉なので、具体的な天気を言った方がわかりやすいです。
例えば:
1)"No cancellations for rain, only cancellations for lightning or heavy snows."
2)"The event will be cancelled if there is lightning or heavy snows, but the event will proceed as planned even if it rains."
3)"The event will not be cancelled for rain, but will be cancelled for lightning or heavy snows."
あと、"cancel"か"cancellation"はイベントに対して言うけど、店・ビジネスの業務時間に対して言うなら"closed"か"closing"のほうがいいと思います。
例えば:
1)"No closings for rain, only closings for storms."
2)"The facility will be closed if there is stormy weather, but the facility will remain open even if it rains."
3)"The store will not close for rain, but will close if the weather is stormy."
また、「荒天中止」があると「雨天決行」はちょっと蛇足な気がするから、簡略化するように下記の例文はいかがでしょうか:
1)"Only cancelled for storms."
2)"The event will only be cancelled if there is lightning or heavy snows."
3)"The event will be cancelled only if the weather forecast has lightning or heavy snows."