Don't worry about looking cool.
However there is a lot to be said for practicing like you will perform.
I play a lot to recordings in my practice sessions. I used to have a very unbalanced mix in my practice room and my drums were much louder than the recording so it caused me to practice more quietly than I would eventually perform the songs I was learning. Once I corrected that (sometimes in a board mix in my practice room and mostly by having louder speakers to my recorded music output, I could play and practice much closer to the way I need to when performing.
As an aside, it was and is still beneficial for me to be able to play well at lower volumes so learning to play quietly has been a big benefit to improving my dynamics on the kit.
Practicing in front of a mirror is a good way to figure what you want to modify visually in your playing style.
Another thing to try is set up your kit with everything a little more opened up and spread out. Practice this way for a while so that you open up your body more and relax your playing style. With everything a little farther away and higher you have to adjust and it may help. It also helps because when you have to play someone else's set up you can adjust easier to a foreign set up with out feeling out of control.
Then when you go back to your "feel good" set up you might look and feel less stiff.
I hope this helps. If you don't choose to change your set up then you can also play along to some slower music that has lots of space between the beats and exaggerate your motions a bit and this will help you get past looking to stiff when you play.
Worry about looking cool after you've mastered the music, if it's still important to you.
Personally, I don't give a crap about how I look because at 6"4" 240lbs I alway seem to look like an ape behind the kit trying to channel some Dave Grohl spirit. At least that is what my wife says.