Imbalanced samples do not fundamentally affect analysis or inference. However, the power of a study depends strongly on the sample size of the smallest group to be compared. Below I discuss ways that, aside from distributional considerations, may strongly improve the generalizability and precision of the analysis. Following these recommendations, any testing procedure you feel is (or isn't) appropriate can be considered. With N=10, the concern that normal approximations are not being met especially with irregular data, is justified. I suspect the variability of the HAQ sample demonstrates some bimodal and skewed properties. That may simply be an aspect of those people: it doesn't imply the mean is not a useful summary, so I might hazard against rank tests.
In observational studies of this form, there are often contributors to the outcomes that are worth bearing into mind. For example, the profundity of autism is strongly affected by age, gender, educational setting, household structure, and so on. With such a small sample, it may sound crazy to exclude participants: but recall the excess of LAQ participants does not necessarily improve power.
I suggest sorting participants to the extent possible based on these factors and obtaining a matched subsample at a 1:1 or 1:2 ratio as you can. You may in fact see there is a subdistribution of LAQ that aligns more closely with HAQ, and thus any form distributional comparison (t-test, Wilcoxon, or permutation test) has greater generalizability and precision.