Is there any cure for wrist pain without surgery?

Depends on cause. Wrist pain can be from a simple sprain to a major problem like fractures ligament injuries and other more esoteric reasons; would need to know what one is treating.
Yes. There are dozens of well described sources of wrist pain. Many do have non-surgical treatment. There are a few that if not diagnosed and treated can lead to crippling permanent problem. A scaphoid bone fracture and a scapho-lunate ligament tear to name two. I suggest you try simple types of home therapy for tendonitis or arthritis and if not a lot better in a week then seek out medical assessment.