1) Those standard deviations aren't so badly different.

2) Since $n_1=41000$, and the standard deviations aren't very large, even if the variances were *very* different, *it wouldn't matter*. 

You could even treat the mean of the first sample as fixed (it almost is) and do a one sample t-test. 

3) The skewness likely won't matter much either, unless it's quite strong in the smaller sample. (you say 'skews above 10 ... but that doesn't really say how big they are. If, say the skewness in the small sample is less than 20, the distribution of the mean should still be close to normal)

--

The Welch test should be okay.

Another alternative is to consider a permutation test (the standard deviations aren't all that different) or a bootstrap test. They'll likely give very similar results to what you already have.