The problem with a chain breaker is it will do just that - break the chain, or the link you're using it on in this case. You'll need a new master link then, and it should be the same brand as the chain so it matches up perfectly. I don't know how easy it would be to find one of those, especially for some off brand chain like yours. Some further research seems to indicate you have a LeMans brand chain, just a basic replacement that PartsUnlimited used to market. Notice I said "used to". It looks like they aren't sold anymore so good luck finding a new master link, lol.
As others mentioned, I think I'd just be using a hammer on the pins. You don't need to move them in much, just enough so you create a space between the side plate and the chain links the master link connects. Then you can quit hammering on the pins and start hammering a screwdriver down into that gap between the plates. I would use a screwdriver big enough to span both links being connected but small enough to slip in between the pins on the master link.
As others mentioned, I think I'd just be using a hammer on the pins. You don't need to move them in much, just enough so you create a space between the side plate and the chain links the master link connects. Then you can quit hammering on the pins and start hammering a screwdriver down into that gap between the plates. I would use a screwdriver big enough to span both links being connected but small enough to slip in between the pins on the master link.