The only products where you could probably do this are in the S&P 500 complex: SPX/SPY/e-mini options because you can hedge your vega with VIX futures or ETFs. Don't think DIA or Dow futures have a liquid Dow VIX contract. But the Dow and S&P 500 are pretty highly correlated, so just use VIX futures or ETFs (VXY, VIXY. etc) to hedge your vol exposure. Just make sure you get your hedge ratios correct.
I am sure this is not what you are asking for as I sensed you know more about options than I. But here it is anyway: If you don't care about delta, gamma, then, it is simple math. If you are long Vega, you can create a zero Vega combination by taking a position with short Vega of the same magnitude. If you also want to hedge delta and gamma, in theory you can create a combination with zero delta, gamma and Vega by solving for zero delta, gamma and Vega. To maintain, you have to dynamically hedge. Of course the devil is in the details. As an amateur retail, this is way beyond what I do.