Unlike the other guys, I always polish the nickel plating on all my HMV's (and pretty much every other machine I own). The only exceptions are those with gold plating, or special finishes like a lacquered or oxidised finish.
The base metal of the arm & soundbox are solid brass, and those dotty patches you see along the arm are verdigris seeping through the plating. If you leave it, it will only fester & permanently discolour the nickel over time (if it hasn't already), & eventually it will cause the plating to lift.
I normally remove the verdigris with brasso, then finish off with silvo. Silvo should be fine for the other parts, unless there's patches of rust (on the turntable rim, speed control etc), then you might have to try brasso, and possibly applied with fine steel wool if the rust is bad.
You wont be able to polish out any discolouration on the nickel, but it will make it less noticable.
Even using steel wool, I've never worn through the nickel plating unless it's a horn machine or lidless table model where the nickel has been constantly exposed to dust etc, and the nickel is badly corroded. On machines where the nickel has been protected, they will usually polish up like a mirror, but after a couple months it looses that "brand new" shine naturally due to the atmosphere tarnishing it. I actually repolish all the nickel again with silvo every 2 or 3 years because it starts looking grubby. The only way I've been able to remove nickel plating from an HMV of this era is to use wet & dry sandpaper. Cleaning & polishing the nickel with a quality metal polish that does not scratch the plating will in no way devalue the machine, but it'll look a whole lot nicer.
Personally, I would never lacquer nickel plating (because it was never there in the first place), but I have waxed nickel plating on external horn machines to give it some (invisible) protection from the atmosphere, and to make dusting easier.
I normally dismantle the whole tonearm, and clean & oil the threaded joint, and regrease the ball bearing in the base of the tonearm, BUT the ball bearings can be a real pain to get back into position.
Unless the arm is stiff or grinding as it swings, you're probable better off to just put a couple drops of oil down between the black painted base & the nickel arm.
If you do have to dismantle the arm, just be careful undoing the 2 screws that attach the T shaped bracket to the underside of the tonearm (the bit that supports the front section of the arm & soundbox & stops it falling down on the TT when not in use). You need to give the screws a good shot of WD40 because the screws are steel & they react with the brass arm, causing them to jam in pretty tight, and being such a fine screw, they can easily snap, leaving you to have to retap the hole.
The HMV/Victor No.4 soundbox isn't difficult to rebuild yourself IMO. New mica diaphragms & rubber gaskets are readily avaible from a number of dealers. Below is a link to the service data for the Victor No.4- which is exactly the same as the HMV No.4 except they are better quality metal.
It might be worth reading through, & if doesn't sound like something you can handle, then send it out to be done for you.
http://www.nipperhead.com/old/vic4sb.htm