GH4, which Yongnuo remote will allow for remote camera shutter?

GH4? Hmm, that might be an issue...

Short answer: The yongnuo RF-603 II might work with the right cable. It's designed to either trigger flashes or the shutter, and can receive flash trigger signals from the yn560-tx. I'm not sure from the yn560-iv or yn660, but I think they should trigger the rf603 flash. I haven't found a cable that works, though...

Long answer:
The problem is getting the right remote shutter cable. Panasonic uses resistors, and I can't get my GX7 to trigger from the rf-603 ii + any of the third party cables I've tried (six). It triggers my D5100 fine (with different cables of course), and some of the "panasonic" cables work with other triggers. I'm guessing the resistors in the cable parallel resistors in the triggers, resulting in not correct resistance to trigger my camera. YMMV.

Best results will be with a wireless shutter trigger designed for panasonic such as this one (I don't own that one, though I'm thinking of getting one). I have a bunch of wired, a couple wireless (including the rf-603ii), and a couple intervalometers. Most work on my D5100, but all are hit or miss on my GX7 (mostly miss), except for the ones originally designed for panasonic.

You don't need the yn560-tx with either the yn560-iv or yn660, as they can control the remote flashes. The tx is so much smaller and lighter, though. Whether you want one is up to you. I can use my tx with the rf-603 II + yn560ii, but.... With my 560iii + tx, I rarely use my 560iis any more, and when I do, they're usually just optically triggered (from the 560iiis going off). I've been looking at the yn560iv and yn660, but I'm fine 90% of the time with two yn560iiis + one 560tx, and the 560ii can cover the rest (minus remote power control), so I don't need the upgrade...