A block bootstrap makes sense to me. (If the term doesn't make sense to you, I explain it at the end.)
In order to pick the block size, I would essentially do a grid search:
pick the largest feasible block size
pick a smallest reasonable block size
pick how many block sizes you feel like testing
I'd run the selected bootstraps and see if there was a pattern, and if so, what might it mean. Once that was done, then hopefully you could feel comfortable with just one block size for subsequent use.
I would think that the best block size would be strategy dependent. But of course I could be wrong. I haven't done this in practice -- I'd be interested to hear of real experiences.
What is a block bootstrap?
Suppose you have N observations. A regular bootstrap repeatedly samples the N observations N times with replacement and performs the statistic on each resampled set of data. The two key things are that the sample size remains the same and the sampling is done independently.
The regular bootstrap is good for when the data are independent. But if there is autocorrelation in the data, then the regular bootstrap completely destroys that. In the case of drawdown, autocorrelation is of significant interest.
The block bootstrap keeps a lot of the autocorrelation of the original data by taking continuous blocks of data instead of individual datapoints. For example if we had 1000 (ordered) observations, then we could sample 10 blocks of length 100, or 100 blocks of length 10, or 50 blocks of length 20, ...