Can wife ask share in my self acquired property after mutual divorce?

Assuming you both are Hindus, Mutual Divorce is recognized under Section 13B of the Hindu Marriage Act.

Section 13B states that the parties can jointly move a petition for dissolution of marriage by a decree of divorce in the District Court on the ground that they have been living separately for a period of one year or more, that they have not been able to live together and that they have mutually agreed that the marriage should be dissolved.

The Court shall then record the joint statement of the Parties and pass a First Motion Order giving time of 6 month to the parties to resolve their dispute, however in case the parties are unable to resolve the issues within the stipulated time, the Court shall pass a decree of Divorce. So therefore divorce by mutual consent takes about 6-7 months.

Your wife cannot claim any rights to your self-acquired or ancestral property during your lifetime but your wife can claim a right of residence under the Domestic Violence Act. Moreoever, your wife is entitled to alimony (maintenance) from you which maybe made by way of monthly payments or one time payment. 

As you are mentioning that she is ready to give you in writing that she doesnt want anything from you, then we suggest you should enter into a Settlement Agreement with your wife whereby a specific clause with respect to this can be added that she shall not claim any maintenance (past, present or future) from you. And after the Agreement is executed you can move a joint petition for divorce by mutual consent.