Tube filament wiring question

[R.G.]

Wouldn't a steel (Magnetic) tube be needed to be really effective?

Chuck's right, copper or other high conductivity stuff will work pretty well. It's great for capacitive pickup, and pretty good for magnetic.
There are two mechanisms of shielding, magnetic shunting and conduction/eddy currents. Well, three really, but let's not go into the fields equations. Magnetic materials like iron, nickel, and cobalt work by being several thousand times as easy for an M-field to "conduct" through than free space. Any M-field preferentially jumps into ferromagnetic metals, but some still gets through. It's' like shunting a 10K resistor with a 10 ohm resistor; most of the current gets shunted around the 10K, but some still goes through it. Conductors work by the M-field causing circulating currents in the conductor that make opposing M-fields that try to force the M-fields to stay out. The better the conductor, the better it forces the M-field to stay out.
Iron/steel/etc. are still conductors, but not great ones. IIRC steel is about 6 times more resistive than copper, but that's better than nothing.
There is a fields-theory thing that goes on too. The fields formed on a conductive enclosure force the magnetic and electrical fields to stay in the conducive enclosure walls, not on the inside of the enclosure.This is more effective with higher frequencies, but it happens. A conductive tube isn't a complete enclosure, but it approximates one away from the ends.
For critical uses, like microphone transformer shielding, the makers use alternating steel and copper layers, one inside the other, several layers depending on how much they want to spend on shields.