Type 31 material is quite good for a 40 meter choke. You can also use type 77 or 75 with nearly equal effectiveness on 40 meters. If you need suppression below 40 meters, then the type 77 or 75 will generally be superior.
If you suspect the wall wart, simply put a choke on its output cord as well. There is no downside to trying it.
As always, if you can put a few turns of the wire on the toroid or large bead, you will generally get a more effective choke.
Make certain you have a good common mode choke on your antenna coax cable as well. It is always better to choke things off at the source.
- Glenn W9IQ