It is a situation where declining is not an option.
こんにちは!
ご質問ありがとうございます。
ご質問について、いくつか言い方が考えられますが、例えば、
It is a situation where declining is not an option.
として、『嫌とは言えない状況』を表現できます。
また、
I received a message asking if it's alright to send the order, even though there might be defective items mixed in. Although I'm reluctant because it would be problematic if it doesn't arrive by the deadline, I find myself in a situation where I can't refuse. So, I responded by saying, 'Please go ahead and send it.' Honestly, I'd rather not…
とすると、ご質問にある内容を伝えられます。
参考になれば幸いです。