Weld or heat and bend sway bar?

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Hit the bar with file. If it files easily it means it's a low carbon steel. If the file doesn't bite in means it's high carbon steel and though it can be welded it could become brittle.
If I was going to narrow it I would cut it in the straight areas and then "sleeve" it after cutting the needed amount.
Don't know if you have a local welding shop they could have good advice.