In general, the braid is copper based and the plug cap is steel. You can push the braid back in and drop a drop of solder on the edge where the two come together. Use a tie wrap or wire tie to get the braid small evenly. No need to solder all around, but it wouldn't hurt anything if you did. A shrink tube works fine covering the area as does electrician's mastic tape (it's rubber tape that you stretch to make it adhere to itself). There is also spiral cut tubing that is designed as chafe guard, but use that over the shrink tube or mastic

Good luck