Sell a call for a risk reversal. If you are going to hedge by buying puts then you are saying you think deep downside risk exists. Don't sell deep downside options to finance the hedge. If you are right about your hedge then your financing trade will seriously undermine your needed hedge.
The problem is a hedge limits your risk and costs money, you cannot put on a hedge and then offset its cost other than simply taking it off. Hedge = insurance = cost, you either pay for the partial protection or don't.
If that were done immediately about the same time, that would be a brilliant idea! I never thought about that before.