Using a multi tap transformer

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.

There is no problem with leaving an unused secondary winding unconnected - but be sure to tape up the wires so that they will not accidently short to each other or to anything else.

The 26/26 volt secondary will give you about 36 volts DC, which is over the the Absolute Maximum input voltage of the 7815 and 7915 regulators, so this transformer is unsuitable for your application.