Statutory registers under companies act for a pvt. co.?

Yes.  They are applicable to Private Limited Companies as well.  You can maintain a combined statutoty register and enter /fill in whatever is applicable to you and leave the remaining.

Statutory registers are compulsory for private companies also. In addition to these, make a practice of taking attendnce sheets duly signed by the attendants in respect of Board Meetings as well as Memebers meetings. This will avoid further litigations to aduitors, secretaries and other officers in case of any dispute.