Unfortunately, Wii guitars are not compatible with PS4, and vice versa for any Playstation guitars. The guitars just can't communicate with the different systems, due to certain functionality built into different controllers. If you want to get a controller for RB4, I suggest going for one that's compatible with the Playstation 4, which also includes ones compatible with PS3. The MIDI adapter, from what I understand, would only be needed for an electronic drum set in RB4 (RB3 supports keyboards, but not RB4), so it shouldn't matter whether the guitar is wired or wireless.
With our setup we use a couple of wireless Guitar Hero guitars and a wired RB1 drum kit, and both work fine with the PS4. Here is a helpful chart
that lists all sorts of instrument types, and whether they are compatible on either Xbox One or PS4. Hope this all helps!