Korean grammar question: What is the difference between 'ㄴ 일' and 'ㄹ 일'?

Hello! I have two questions. First, I'm wondering if the sentence '올해는 눈이 덜 글썽거리길' is the correct expression. I'm writing a three-line poem to send to a friend, and I want to start with the letter '글'. I'm worried that this sentence may not sound natural as the expression '글썽거리다' doesn't seem to be used very often. Second, I'm confused about the difference between 'ㄴ 일' and 'ㄹ 일'. For example, I thought that '올해는 우는 일 없길' and '울 일 없길' have the same meaning, but I don't understand why they are used differently. I would appreciate it if you could provide an answer. Please understand that the response may be delayed. 🥲