If this is a linux system can't you just mount a directory from the remote (box 1) filesystem on your on box-2 filesystem, and give the directory rx permission on box2? That's more of an OS/Networking question though.

Update: I apologize for misreading your question. I thought you were asking about how to locally run a file that exists on a different machine on the same LAN, in which case that would have been a pretty good answer. ;) Given that you were asking a different question than what my eyes saw, I provided a poor answer, in good faith.

Ahem... move on, nothing to see here.