Removing neon transformer center tap?
Removing the center tap, even if it was something you could just do, would be a very bad idea. The beauty of having a center-tapped transformer is that each side of the tap only has to be rated for half the total voltage, whereas if you have the full voltage on one end you risk destroying the insulation, and thus the transformer. 

Your best bet would probably be to find another transformer, one that is end-point grounded. Whether it be a neon transformer, an oil burner ignition coil, or (NOT RECOMMENDED), a microwave oven transformer, getting a transformer that is designed to have the full potential on one lead would be ideal.

So my recommendation would be to not remove the center tap, as it could cause all sorts of problems, even ones that you would never expect.