Hi...both the options have their advantages. If you go for surgery, your recovery will be faster but you will have to pay more money.
If you dont go for surgery, the treatment will be cheaper but the recovery may take more time.
Next Steps
Even if you dont go for surgery, there is a high chance that the fracture will heal. But see to it that you get regu xrays...and as per those xrays, immobilize the shoulder or start gentle range of motion exercises...