Hello.
I have bought this cheap Chinese multimeter over a decade ago. Also later bought additional probes from China because people recommended them. Eventually when I lifted both, one of the probes had its cord disconnected from it. Fine. I have probes that came with original multimeter.
Today I wanted to test continuity in antistatic wrist strap because before using it, a small part of shielding came off, exposing the wire at the end. Also happened on the alligator clip's part. Little did dummy me know that it has capacitor that cheap multimeters won't be able to detect the closed loop. There was continuity between alligator clip and exposed wire but there was no continuity between exposed wire and grounding button. I didn't know and assumed that wire got damaged within yellow casing that metal button is molded into.

Long story short the antistatic wrist strap works and shows .983 reading using 2M ohm setting on multimeter. I guess it is okay and it works properly so I can start working with electronics?
I want to fix what I damaged because I am interested in it and I happen to have a crimping tool, ferrules and red sleeves that I have recently ordered. I have sleeves that require a heat gun that I don't have but I have hair dryer and hair curler which when has it's accessory removed, blows concentrated hot air. I also have butane jet lighter.
I am wondering which route should I go to protect exposed wires from being damaged further. Can ferrules and/or red sleeves affect the conductivity to properly keep me discharged from static electricity? Does one affect more than the other? I think red sleeves are for 2.5mm sized wires and not sure if they will fit.

You can also see the solid yellow casing that I cut right before it connects to metal button. Since it still has its cut part in place I was thinking of filling the gap with a glue gun. Would it be okay or I should remove that part and go the ferrule or sleeve route? I will probably still have to apply glue between yellow casing and ferrule to prevent wire from moving?

Thanks