Now I try to discourage pvp at my tables but don't straight ban it. This may be a situation where you don't have a choice in taking him down. Try and find a Non pvp option first, but it sounds like you have and it may not be possible.
Yeah, the unwritten rule of a no-pvp game is to not do things to other players that, logically speaking, should result in pvp. Really, calling games "No PvP" is a bit of a misnomer in my experience. Usually, it's not so much that the GM is fine with anything up to actual attack rolls against other PCs, what he really means is "No major inter-party conflict or drama."
In that light, trying to expose undercover members of the party and ruin their operations is every bit as much of a hostile act as actually swinging a sword at another PC.