I've broken a few fans like that.
You're right. Either a new fan or an entire heatsink and fan combination to fix it.
These fans range from only this fits to generic. Since we have no pictures to work with I can't guess. But I have replaced just the fan at times.
So recently a blade of my heatsink fan broke off. It now sounds horrible with a sound output of appx 70 db.
According to speedfan, the core temperature was at about 37 degrees celsius, but this morning when i booted it up, and opened firefox, i got a blue screen. I am wondering whether the blue screens are due to the cpu temporarily overheating, and a replacement heatsink/fan will fix it, or whether a new cpu is necessary.