I don’t think it needs a spacer for 10 speed….but it will need a spacer on the backside for a 7 speed cassette.
Also, the 126mm rear spacing, if it is, and it might be 120….the 126 will accept your 130mm rear axles with hardly a blip. When 130’s came out they actually had a bit of a bevel so you could fit into a 126.Forget all this “cold set” of bending the frame. If your rear dropout has a set screw in the back you use that to center the axle. My 92’ Schwinn Paramount with 126mm rear has been running Ultegra 6500 wheels for the last 15+ years.
__________________