IMO a low/no carb diet isn't the way to go. Some of my friends have tries a low carb lifestyle and did manage to lose weight, but as soon as they started eating carbs again their weight ballooned back to the norm plus more. Also, your body uses fiber to aid with fat loss and digestion.
In any case, recomp is the way to go. Don't try to focus on cutting or bulking, those are simply shortcuts which can carry negative consequences. (fat gain, muscle loss)
I would recommend not trying to gain a significant amount of muscle while you lose fat, as this is nearly impossible without kick ass genes. Instead, focus on very slight and slow weight loss with increased strength.
Here's how: Find out exactly the right amount of calories needed for you to remain at the same weight. Eat well, high protein, moderate carbs and moderate fats, every two to three hours. Drink plenty of water. After you have that down, add a cardio session for every day that you are not lifting.
I know it sounds hard, and it is, but really try to push yourself farther and farther each time in the weight room. This will boost your metabolism as well as keep your strength from going down.
You can do it bro, I'm actually following these steps as well and it's really working for me. I started doing this about a month and a half ago, since then my bench press went up 15 lbs and my weight dropped about 3 lbs mostly fat.
I've left out a lot of details so just let me know if you need any help or other information.