Agree

如果用whether
Please let me know whether you have any further questions.
"不管有無問題,都請告知"

Please let me know if you have any further questions.
若有問題請告知(沒問題,就不讓我知道了沒關係！！)

不過....樓主問的其實不是"文法"
而是英文的"表達方式",(或說英文表達邏輯？)
當然樓主文法也有問題就是