Question about transformer current

For the power level you need, the transformer can be small, here is an example part (yours would be the smallest, datasheet here with dimensions):

You'll note it says 2 x 5V for the secondary, but you only have to use one of the secondary windings.

For a switching supply, here is a small module that takes 85V-265V and outputs 5VDC, the dimensions are 26.7mm by 31.7mm:

Here is an example schematic, based on a teardown of the iPhone charger:

The above came from this site.

The input transformer is required for electrical isolation. Do NOT remove it!

This circuit is similar to the old tube-type AM radios from years gone by. The circuit operates directly from the incoming AC power. If you look closely, you will see that one side of the incoming AC power cord is tied directly to the main circuit ground.

Although the AC plug is marked with (-) & (+), there is NO guarantee that you won't wind up with the incoming hot (Line) conductor connected to the circuit ground. This is a potentially lethal shock hazard should anyone touch both circuit ground and an Earth ground.

The input isolation transformer simply couples the desired input signal to the volume control while providing galvanic isolation.

Note: the metal shell on your 1/4" Phone Plugs on the guitar cord as well as the metal faceplate on your guitar are all exposed and can be touched. Do NOT remove or bypass that input transformer!