I'm not sure, if not hamachi then I wonder if it would be possible to have another software do something like this.
'cause your computer and your 3DS would be on the same local network, so I wonder if there would be a way for the computer to kinda put the 3DS in another local network with someone else's 3DS over the internet.
I mean, this connects via internet but apparently only uses local IPs or something? I'm not too savvy when it comes to that so I don't know if there could be a way to "forward" a local ip like this to the internet somehow.
That or maybe see if it'd be possible to modify ctrquake to use actual public IPs.