Fully isolating output ground on Sola CSV Transformer

Hello. I'm new here and greatly appreciate any assistance that more qualified persons can provide. I am a DIY person with some, but limited, experience handling transformers and other high voltage items in electronics. I have a deep respect for their potential to harm and I like to be very sure about how things may impact a project before I attempt any such work. I do know the basics of being very careful with such project, hand behind back and not touching things indiscriminately, etc., but I want to ensure I'm thinking about grounding principles correctly on something I'm working on.

I would like to fully electrically isolate from ground the output of an older Sola CSV Transformer that I have (an old version of Model 63-13-210). I am doing this as I want to use the transformer as a ground isolated power source feeding into a variac unit, which will feed variably increasing voltage to a relatively small (less than 50W, probably 15W) tube amplifier project I am building.

My question is, am I correct that if I:
(1) replace the output receptacle with a ground isolated receptacle, and
(2) eliminate BOTH of the wires that are currently connected from the receptacle to the ground bolt (in the close up photo, the two wires all the way at the top left) (and, for clarity, I would leave the lead from the input plug to that ground bolt intact),

then will I have an electrically ground isolated output that will not create inherently dangerous conditions with respect to the transformer internals, the chassis or the subsequent load items?

Many thanks for any help you can provide and my apologies if any of this is not clear or if I am on the wrong track. I ask to learn. Thank you.

Gratefully,
Leo