Due to everyday pull-ups I've got pretty bad calluses on my hands.
Is there any way to escape them ?
As long as you are doing pull ups bare-handed you will probably have a hard time avoiding the callouses. And if you are continually cutting down on the callouses that you already have you may find that your hands become a little raw in the areas that are critical for gripping the bar. This might end up compromising your workout.
I recommend getting some gardeners gloves (I workout in the park in NYC and almost everyone wears these) or some baseball batting gloves.
They provide great protection and will keep your callouses under control.
One, you can use something like Lanacane to cut down on the callous you already have. Two, and this is what would really work long term, make sure you start in the position that your hands normally slip to. This applies with dumbbells and barbells as well. Find the end point that the bar would be in your hand, and make sure that's your starting point as well. If your hands aren't slipping around, you'll have much less of a callous building up.