Wire
The wiring in your Equasonne is cloth covered and is generally pretty durable, though it tends to become brittle over time.  If some of the wiring needs replacing because it looks too frayed and untrustworthy, or if it has been previously cut and spliced in long ago repair jobs, similarly styled cloth covered wiring is available in various colors from several sources.

The wiring that tends to become the most mangy over time is the power cord, the 4 wire cable that runs from the power converter to the speaker, and the 8 wire connecting cable that runs from the RF Amplifier to the 9 post connecting strip on the side of the power converter.

So far, I know of no supplier for an exact replacement of the original thick cloth covered power cord. 
Antique Electronic Supply does sell some attractive brown cloth covered 2 conductor power cord that although much skinnier than the original power cord, will do the job.  Currently, they actually sell two types of cloth covered power cord.  Power cord S-W103 is sold at $2.50 a foot, and although it is the thicker of the two cords they sell, it is only marginally thicker than the S-W102-20 cord that they sell at $8.25 for 20 feet.  The second choice is the much more economical of the two.

The 4 conductor speaker cable can be easily replaced using some cotton covered multi-conductor cable also sold By
Antique Electronic Supply.  They sell this cable by the foot.  It contains 8 differently colored braided cloth covered wires, contained in a brown braided cloth cable.  Simply cut a piece to the appropriate length, pull out 4 of the 8 wires from the cable, pull on the outer brown cloth wrapping of the cable to readjust it to the skinnier diameter of the cable and there you have it!

The 8 conductor connector cable that joins the RF Amplifier to the Power converter can also be replaced using
Antique Electronic Supply's 8 conductor cable, but unfortunately it requires a bit of modification first.  The wiring in this replacement cable is 20 gauge, which is OK for most for the circuits, but no so great for the filament heater circuit for the 484/485 tubes (circuits 1 and 3).  For this I used  16 AWG wire.
With patience and perseverance it is possible to remove the brown outer cloth wrapping from a length of this cable, remove 2 of the 8 cloth covered wires, replace them with 2 lengths of 16 AWG wire, then slip the outer cloth covering back over the 8 wires.  The spade terminals for the connector cable can be purchased at most electronic stores, you need size #6.

Alternatively, if the outer black cloth covering of the original 8 wire connector cable is still in acceptable shape, the 8 original wires inside the cable can be replaced one by one with new wire, leaving the original outer black cloth covering intact.  This is in fact much easier to do than creating an entirely new 8 wire cable as described above.  Cut the end off each original wire and strip back the insulation about 1cm.  The exposed metal wire will have oxidized over time, and must be cleaned until shiny using steel wool or sandpaper or it will not accept solder.  Do the same with a length of new replacement wire.  Intermesh the two wires end to end and solder them well.  When cool, test the strength of the joint by pulling on each end of the joined wire.  Wrap the joint in a short piece of masking tape, then use the old wire to pull the new one through the outer cloth covering to the other end of the cable.  Replace each of the 8 original wires in this manner.  Cut the 8 new wires to the exact length of the originals, solder a #6 spade connector on the terminal attachment ends, and attach the other ends to the appropriate spots on the RF amplifier circuit board, and you are done.

Any other miscellaneous wiring in the set that needs replacing can be done with cloth covered wire obtainable from:

Antique Electronic Supply does sell cloth covered hookup wire on spools as does Radiodaze. However, I purchased a length of AES's 8 conductor cable, and dismantled it to produce 8 lengths of different colored cloth hookup wire before I discovered Radiodaze as a source.  Although this certainly works, it is not the most cost efficient solution as this 8 conductor cable sells for $3 a foot.

If you decide to open up and rebuild the large filter can capacitor you will want several lengths of cloth covered wire to make the leads.