True story from my side. I been to this interview recently, i provided my pay slip too. When the offer came, it was about 20% increment. However, i bargain to the extend of 80% increment. It does takes sometime to nego to this figure.

My opinion is that you have nothing to lose by providing your current payslip. Now you walk away an opportunity without knowing what they going to offer you. They can offer whatever figure to you, if you happy, just take it else just walk away.

I am same like you. I am comfortable at my current company. Just want to go out test market. Just stand firm and be confident about the expected salary / figure.