There are a number of different ways that adding a 3-prong cord can be done as far as the fuse and switch are concerned. For example, Marshall uses a double pole switch for both legs of the AC and puts the fuse on the hot wire, Soldano swtches the hot only and fuses that side as well, Dumbles and many others fuse the neutral and switch the hot. Just make sure to attach the ground securely to it's own bolt and don't use a "death cap" or polarity switch setup.
There are variations in standby switch setups as well that you can see if you look at a bunch of different makers schematics. Some put a switch directly after the rectification, some put it right after the first filter cap ( but still before the OT CT). If you are going to switch the B+ like this for the standby function, then you should put a .01U 1000V ceramic disc cap across the standby switch to prevent popping when you engage it.
The other way to do a standby is to put a switch between the CT on the secondary of the PT and ground like many Ampegs did for example. I have read that the purpose of this is that it keeps AC on the switch and is easier on it.
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Lots of pros and cons about standby switches.
Some of the guys like the Valve Wizard say you don't need them on a audio amp.
They say it is a left over from powerful radio transmitters so people just kept using them.
Depending on whether an amp is tube rectified and whether or not the cathode is directly heated or indirectly heated is another thing that affects the warm up.
It is said that tube cathodes reach operating temperature in as little as 15 seconds and that cathode stripping or cathode poisoning is really only a factor in larger equipment like radio transmitters.