I share a broken fence with a neighbor but I don't want to pay my portion of the cost to get it fixed. I think I'll just fix it as cheaply as I can.
Why don't you want to help pay for the fence?
I need to save money
I understand you want to save money, which is good to do.  That being said, you need to find a way to do it that doesn't involve deliberately paying for something substandard, especially when it's a shared item.  Your neighbor sure wouldn't appreciate you being cheap on this!
No way, if they want to pay to get it fixed by a professional, that's their choice and their problem.
I'd just caution you that it's often more cost-effective to pay to do something right the first time. If you cut corners fixing the fence, you'll probably need to repair it again very soon. Perhaps, you can pay for the repairs in installments.