Hello, first of all, normal vol is F*black vol only for ATM strikes. For everything else you need to use a more exact approximation (e.g. the one by Hagan), but for close to ATM strikes, sqrt(F*K)*black vol is acceptable as well.Secondly, if you want to keep normal vol constant, as you state in your example, then you should use a normal model for hedging. Thirdly, if you insist on using a lognormal model which requires a smile to correctly price the market, then you should really use a stochastic volatility model, e.g. SABR, which then gives you a much better term for what you call "(black vol new - black vol)*vega".On a related note, I think you may be confusing the meaning of the smile for hedging. The smile roughly represents the average of the local vols up to expiry. It does not represent the local vols themselves. So there is no need for what you call "new black vol" to be equal to blackvol*F(F+1). In fact, if the market implied vol is correct (in the sense of mkt efficiency), then you can hedge keeping this vol constant until expiry.Also, I dont understand why you mention spot rates. They dont enter at any point (exept for building the curve that you need to interpolate the fwd rate). What do you mean by projecting back to the swap curve?