The problem you are facing is the simplest of simple one and so accept my advance marriage best wishes.
To avoid any problem, you and your love go to Arya Samaj Mandir in Pune and both being Hindus, your marriage will be solemnized there as per hindu rites and customs. They will not inform to any one. They guide you the entire procedure and your marriage will be registered and a certificate will be issued. This is a valid marriage for all the legal and practical purposes. This is enough. If you want to be double sure, you take sufficient photographs of solemnization of marriage and on the next date meet the marriage officer under Hindu Marriage Act and fill up the application and supporting documents. This can be done in Pune itself. Your marriage will be registered instantly and one day after, you will get marriage certificate under Hindu Marriage Act.
The marriage you are talking about is "special marriage Act" and there one month advance notice will be sent to the permanent address of the parties and also notice board pasting will be there. Delhi High court in 2009/2010 (Justice Ravindra Bhat) passed a judgment that if any one of the parties object for such kind of notice to the parents of the parties, the notice shall not be sent. But it is very difficult to get approval of marriage officer under Special Marriage Act to follow the law laid down in the judgment. So, my suggestion is to go for Arya Samaj marriage and immediate registration under Hindu Marriage Act.
Again advance best wishes.