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. Very nice quality reproduction cloth covered power cords, and vintage style plugs can also be had from Sundial Wire, and Grand Brass.
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! Radio Daze also sells similar cloth covered cable, with either 4 or 8 conductors. With the 8 conductor wire, you can pull out 4 off the wires, and stretch the cloth outer covering out to make a snug fit. I like to remove 5 of the wires, leaving yellow, red and blue, then insert a second piece of yellow to recreate the color scheme that matches with the color code on the back of the speaker. makes it much easier to figure out how to hook it up when you are done.
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, or that from Radio Daze. 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. The long lead wires to the volume control and to the on/off switch will usually be found to have hardened up and the insulation to have cracked in several places. It is worth replacing this as well.