Having worked for 35 years at Hobart I have seen numerous loose laminations and removing one lamination does not affect the workings of the welder.
With all due respect to your 35 years at Hobart;
1)sliding a lamination out of this enter of a transformer, and risking damage to the delicate varnish insulation of the winding, does not sound like a good solution to the problem,
2) reducing the core thickness by one lamination's may not change the specs of the transformer much, but it WILL change it some. It was designed with a particular core size with a particular number of lamination's for a reason. It may not have the impact of making a change to the winding's themselves, but you will lose a bit of the tight proximity of the wingdings to the core, as well as some of the mass of the core. I don't believe that wouldn't have an affect, having been deeply involved in the design and manufacture of more than a few wound inductive devices in my career. They may not have been of the size and capacity of a welding transformer, but the electrical fields are designed to a spec and a tolerance. Changing any part of it will affect the output to one degree or another.