from http://www.teamxlink.co.uk/
XLink Kai: Evolution VII is the third and final application in the XLink series of console tunnelling applications. Whereas in previous versions, online support was only available for XBox users, PlayStation2, Gamecube and PSP owners can now join in on the fun.
and there is only one package for all, so i guess it should work for the psp to.
but i don´t think that there is a webinterface or something like that, so you need to run a ui somewhere else. there is a ncurses-interface which you should be able to through ssh on the router, or you use another gui.
I not sure if there is a GUI to run on the psp, but you should try running the daemon in your router and connect with a ui from your windows-, linux-workstation, or whatever you use. so it should be the right application but you will need to configure it to run with the psp.
and I think if you don´t get a image in which it´s working out of the box, than openwrt would be your best chance to get it up and running.
you have a writeable filesystem, plenty of flash-memory left and there are a lots of packages available, and it´s very stable.
you just need to copy the kaidpackage to the router, edit the configfile and start the binary. then you can connect with a ui from a remote-computer, or the psp (if there is ui for it) and configure it.
I don´t use it, but it seems like the ui and the daemon is separated just fine, so there shouldn´t be any problem to run it on a router.