I'm not really sure why you'd send an emulator with it, seeing as they'd need a patcher to play a romhack anyway and they could just download what they need while they're at it. Unless you're distributing roms.
Anyway. The ideal target for "just put it in and run it" is Mesen by far, and it's also the best target for development/most accurate NES emu. Another good point about bundling it with stuff is that it auto-updates. The worst part is that there is only a Windows binary, however it exists as a RetroArch core that works just as well but last I checked there were issues with it working on Mac (this was also quite a while ago). Nestopia would be an alright replacement if the mapper is in there, but the binary for that is also rather old as Nestopia UE is the continuation of it. Keep in mind that Mac has OpenEmu with both Nestopia and FCEU cores out of the box; it's easier to use but RetroArch is still there. Sure there's Mednafen, but not having a GUI is usually a good way to get first-timers confused no matter how easy to use it is.
One thing though: do not make a romhack with the officially released FCEUX found on their website in mind as it is four years old, use devbuilds compiled elsewhere instead.