Apologies for the delay on the hedging of non-forward-starting volatility swaps, but it's only since this week that I have an answer for this.
So, for plain volswaps, I can give you a nonparametric hedge in terms of varswaps only. That's not as cheap as using a single option (which I believe is not possibe anyway), but certainly better than trading an infinite number of options.
Nonparametric, as you know, meaning the hedge ratio does not depend on the particular SV model, i.e. model independent.
The link below gives the hedge. My contact details are at the bottom of the title page if you have questions.
Nonparametric Hedging of Volatility Swaps with Variance Swaps in StochasticVolatility Models by Frido Rolloos.
Please note that the paper has been updated (same link) with a more accurate and novel hedging formula and numerical simulations. Below is one chart of hedging error taken from the paper. A hedge P&L of say -0.3% means that the difference between the replicating portfolio / hedge and the terminal realised volatility is for instance 19.7% - 20% = 0.3%.