Download the latest development build of Dolphin, then enable Relative Input. (Relative Input was added very recently, so it's not available in 5.0.)
If you want any of the development builds from https://dolphin-emu.org/download/ to be portable, you just need to create a file named portable.txt in the same folder as Dolphin.exe.
If you want any of the development builds from https://dolphin-emu.org/download/ to be portable, you just need to create a file named portable.txt in the same folder as Dolphin.exe.