It looks like Browser Stack has a free trial. Does that not include Safari 9 testing?
The only other “free” method I can think of is to find someone with a Mac who doesn’t mind their computer being taken over temporarily. Either in person or remotely. I’ve used Join.me before, but can’t tell if the mouse control feature is free.
Otherwise, I have to agree with @Senff. I get the sense this isn’t the highest priority for you, but if you care at all about fixing this problem, would you rather buy a Mac for $500+ (starting price of Mac Mini) or pay $25 for temporary access? Even if its for just one problem, it seems like a no brainer to me.
Who knows, maybe you’ll uncover bugs on other browsers that make it seem more worth it.