I have a PC that has far worse specs than yours (dual core lol) and I can play and record at ~100FPS, the trick is using your integrated GPU which in your case would be Intel to do all the heavy lifting and letting your CPU cores and discrete GPU handle the game.
I only tried and used OBS and never had any issues with it, I can give you a few tips to setup yours so it has a good balance between quality and compression.
