Instead of thinking about conversion, Just let VISA come and you can always apply for Rupay later on..
Don't think you are going to miss out on anything... After a month you can get Rupay very easily...
Let this dust settle...
Give some 3 to 6 months time and request ICICI thru twitter.
Or
Start spending on your existing ICICI CC, small frequent spends..and check your IMOBILE app for pre approved offers , try occasionally uninstall, reinstall IMOBILE App to see if the preapproved offer appears