For some reason it recorded upside down. I used the GoPro editing software to flip it around. I noticed that but wanted others to hear the noise. First time I have ever heard it. New brake shoes are only $18 from Yamaha. Not bad. 

Sounds like after 20 years it is time to change the shoes. New tires and now brake shoes. I guess the old girl deserves it. 

I had another listen & couldn't hear it untill the last bit coming in your drive just before you stop moving.
So I slowed it down to 1/4 speed & the last 3 squeels you aren't pulling on the lever [lever being the left one back to front].
I can see enough just at the end to see your right leg probably isn't on the rear brake so [head scratching] i don't know. But noise isn't brake shoes on the drum, but are they overly wide aftermarket shoes touching the hub in there in the back.
Are the wheel bearings ok. Thinking wheel moving slightly on bearings & shoe sides touching casting bits in the hub.
Is it the "speedo drive"--if it's that dry its a wonder it's still turning.
Maybe it's dry of grease where the big gear turns on the hub, not the cable gear.
There's a big seal that needs a light wipe of grease too sealing off the speedo drive.
One more try--Front brake cable can squeek sliding through the cable guide as the forks go up & down but not had that for a while on anything but was quite common wheeling mostly smaller bikes into the workshop & could just move them up & down a little on the forks & they'd sing away.
But yours isn't that as is cyclic [is that a word] coming in your drive.
I'll stick with speedo drive noise--pretty loud though so probably not.
Just a minor edit--i just realized i was looking at the wrong knee for leg applying the rear brake in the last second or two.

Do I put some lube in the speedo cable or down at the hub drive?

These cables were brand new when I did the full restoration 7 years ago. I don't think I changed the wheel bearings when I had the wheels polished and restored.

When replacing the shoes is it recommended to replace the brake springs as well?

Yamaha shoe sets come with new springs. 

Wonder if springs are touching the hub center if the center has a slight casting imperfection. If they're aftermarket shoes & fat springs for example.
Speedo drive gear the wheel turns--has the drive plate with ears & is retained by a circlip. Pull the gear & wipe a light smear of grease where it revolves & on the gear helical teeth.
I don't think that's the noise though. Speedo drive other gear is a problem to get out without the right tool but unlikely noise coming from there.

These brakes were OEM I believe. This squeak has not been there ever in the last 20 years I have ridden this motorcycle.