I own over a dozen cameras that originally took the PX625 1.35v mercury battery. To feed them now, I use 675 hearing aid batteries, which I buy at Costco. They come on a card for about $10 -- used to be 40 per card, but now I think it's 48 per card. These are zinc-air batteries that put out 1.4v -- close enough. The downside to zinc-air batteries is that they don't last very long. Usually 9 or 10 months, tops. But they're so cheap, I just keep a card or a portion of a card of the batteries in my bag so I'll always have plenty of fresh ones when I need them.
The 675 battery is smaller in diameter than the PX625, but about the same thickness. This smaller size typically isn't a problem. Most of my cameras make contact with the + side of the battery from the battery's face. And most of these cameras have some sort of spring pressure than holds the battery in place, so I can usually use the battery as-is, since the spring pressure holds it into position. But in situations where that isn't the case, in order to center the 675 into a PX625's socket, I use a piece of ~20 ga wire -- about 1" or so long -- coil it up and set it into the bottom of the battery well. This is enough to keep a 675 battery centered. O-rings of the appropriate size also work. You can usually find a good assortment of o-rings at an Ace Hardware, or the like, to find the size you need.
I own a Yashica Mat 124, which is essentially the same camera as yours, but I cannot recall offhand exactly the way the current is picked up in the battery compartment. If the + side's contact is with the face of the battery and not the side, then I just use the battery as-is, or if necessary, with a coil of wire. If the voltage is picked up from the side of the battery, then things get trickier. The easiest way to handle this is to buy metal adapters that will fit the 675 and convert it to a PX625's diameter. You can buy these from a variety of sources, but I prefer Jon Goodman, the fellow who also makes the light seal kits for the classic old cameras. In a pinch, one can make a substitute for the ring adapters buy cutting out a strip of aluminum foil, folding it up so it's the right height, then coiling it around a 675 battery. I've done this. It's somewhat fiddly, but it works.
Finally, is it worth it, going to the trouble to power the meter on a Yashica Mat? Well, I've owned a 124G in addition to the 124 I own now, and I can report that I have used both camera's onboard meters many times and I've always gotten correctly exposed images. But for any sort of critical work, including shooting slides, I've always used a hand-held meter and/or a spot meter just to be sure. But yeah, for general shooting, I don't have a problem using the Mat's meter -- as long as it tests out to be accurate in the first place.