How can a toroidal transformer be sited within a wire nest?
What you want to do is OK as long as there is no conducting loop thru the center of the torus and back around the outside.  A simple way to guarantee this is to put something insulating in the middle of the torus so that nothing conducting can make a complete loop that includes going thru the middle.  A piece of cardboard, plexiglass, phenolic, circuit board without traces on it, etc, would do it.

Toroidal transformers are pretty good at containing the magnetic fields, but some will still be present outside the torus.  Something conducting immediately outside the torus will pick up the stray magnetic field and will have some eddy currents thru it.  Those should be nowhere near strong enough to cause excessive voltages or heating.  They might be strong enough to upset delicate analog circuitry though.  Keep such things a full major radius or so from the outside of the torus.