Is a spring steel blade very wobbly(I hear it is)
No. The whip of a sword blade has a lot more to do with it's shape and design than it's material.
Normal sword blades are made from spring steel. They pretty much need to be in order to be functional. Spring steel is just a generic term for medium and high carbon steels that are capable of being hardened.
^ what Sir Ian said.
Also, find whoever told you that, and correct them.