I wish to try out a technique which my supervisor does not want me to, because its not his expertise
This is a question you can only answer yourself, because it's about the balance between working on stuff your group is experienced in and trying out new stuff. But let's list some arguments why you should not go off doing something just because it's interesting: 


You probably have a Phd topic yourself, and every month spent on something not directly relevant means you're defending a month later. Will this fit in another publication you're planning to write?
Your supervisor is not an expert in this subject, which will definitely cause you to make some avoidable mistakes that will take time or make the project weaker. If your supervisor cannot help you, do you have someone else that can guide and teach you?
Even if it's a new and fancy technique, new and fancy doesn't do anything for you if you're not an expert already. You'll probably figure out stuff that has been figured out already. Will it bring direct results that you need for your other projects?
You'd not be doing this project in magical extra time, it's something you'll be doing instead of something else. Is it really that much more interesting than something closer to your expertise / project? 


Your Phd is about doing research. Bringing projects from start to finish and publishing. Not about learning for the sake of learning. You probably did enough of that, now it's time to push the boundaries of knowledge.