I know next to nothing about this kind of thing, so hopefully someone more knowledgeable will chime in here, but you might look into registering as a Nevada corporation:
http://en.wikipedia.org/wiki/Nevada_corporationThere are a handful of benefits to incorporating in Nevada, not least of which is that the entire process has become its own sort of industry, with other businesses set up just to inexpensively help you work out the paperwork and maintain the necessary legal presence in Nevada for you. One such service (http://www.incparadise.net/) specifically says that you don't need to be a U.S. citizen or have a U.S. address to register as a Nevada corporation. That plus a mail forwarding service (also offered by the same company) plus a few other magic tricks should let you get set up with Stripe -- I've never tried that though, so don't know for sure.
Might be something to look into, anyway. Certainly a lot cheaper than finding a co-founder.