"Due to work, I don't think I can send it until next week."
"I think I can send it next week." は正いですが至急連絡の場合には使われません。
- "Due to work, I don't think I can send it until next week."
"Due to work" 「仕事の関係で」
"I don't think I can send it until next week." 「来週まで荷物を送ることができませんと思います」
"I can't send it until next week." 「来週まで荷物を送ることができません」も大丈夫です。
"due to work" や "because of work" という理由の後 肯定的より否定的の方が適切です。なので "I don't think" や "I can't" を使われています。