You have two choices:

1. Change the data sources to use a SQL login and password, then you can use the built in subscription method.
2. Use a scheduled app to generate the report, and have that do the e-mailing.  The scheduled app would need to run under an account with permissions into SQL/SSRS.

I would only recommend #2 if you don't really need/want the users managing their own subscriptions.  If the users are going to need the ability to generate their own subs then #1 is your only real option.