Just to be clear...  the danger is not just that one brake or the other might fail to slow you down if they delaminate...  it's that the wheel will almost always lock up solid without notice.  If front wheel locks up, rider can be thrown over the bars or best case you can hope for is you will crash.  Rear wheel lock up is possible to ride out...  but still dangerous. 

If you can only afford one set at a time, definitely replace the front first. 

It's like 50 year old tires that haven't been used. They may look great, but they've degraded over the decades. I found some huge cracks on my 50 year old tires, after unmounting them. The same with brakes. Adhesives break down over time. Mine only had 320 miles on them, but I replaced them to be safe.

Appreciate the responses. We'll replace both brake shoes now.

We're going to tackle the rear wheel today. The front was pretty easy. The rear looks a bit more complicated. Below are the steps from the manual. There isn't much meat to them  . Any additional tips or anyone know of a video out there? 

1. Remove the tension bar and brake rod from rear shoe plate
2. Disconnect the drive chain...how?
3. Remove cotter pin from rear axle
4. Remove the rear axle nut
5. Pull out rear axle by simultaneously twisting and pulling out.

The chain should have one link with a "U" shaped clip on it, sitting over a plate - unclip the link, remove the plate and the link out.

When you re-assemble, MAKE SURE THAT THE CLOSED END OF THE "U" CLIP IS FACING FORWARDS WHEN YOU ROTATE THE WHEEL IN A FORWARDS DIRECTION!

 Video removing master link.

Good video wish my shop was as clean as yours 

Ht1kid, it's not my video. I really like the way he does it, with the master link braced on the sprocket, making it easy to knock the clip off with a screwdriver. I've usually done it with the link off the sprocket, using regular pliers.

Take plenty of pictures as for the orientation and placement of the wheel spacers, and it might just be me doing things incorrectly but I don’t think I have ever removed the master link to remove the chain and remove the rear wheel, too much risk for that clip flying off somewhere (like in posted video) and then having to buy a new master link, and like everything these days there are dozens of options on master links depending on chain manufacturer, size, oring, non oring. Orientation of master link clip is important as is top side and bottom side of the stamped master link clip (like a “c” clip or”e” clip), I usually just back off the chain adjusters, pull the axle and it all falls down with the brake plate, change tire, rim strip, tube and reinstall in reverse order with chain off of rear sprocket, once axle is reinstalled walk the chain back on the rear sprocket and rotate wheel and the chain is back on, (like in posted video) I might be steering you in the incorrect way to do it but I have done it that way dozens of times from bicycles to big motorcycles. Being a 125cc it is a small chain and will “walk” back on the sprocket easily. Maybe others will chime in on their preferred method?

Yes, Lizeec's is a perfectly good way of doing it.

Bottom line, there's more than one way to skin a cat, whatever that old saying means :o)

I mean, has anyone ever skinned a cat, and if so, why?

Anyway, my adjusters have very little play, since I went up one tooth on the countershaft sprocket Also, the guy in the video could have contained the clip simply by cupping his left hand over it, but that would have hid what he was doing. "Whatever works", is my motto.