Is a soundproof stud wall made of 38 x 63mm CLS strong enough?
You could always use the lumber you have and reduce the spacing to something like 5 3/4" (that's the actual spacing ratio for a 2x4@16"oc) to get an equivalent amount of control over the deflection. 

I would not use anything less than a 2x4 at 16" on center, or it's equivalent. The main reason for this is because if someone were to lean on that wall they could crack the boards on either side. This would not only ruin their appearance but it could reduce their acoustic performance. Additionally, if a seismic event were to occur the weight of all that materials you have on there would begin to move with the earthquake. It would bend the wall out of plane causing cracks. 2x4s at 16" is the code recommendation to avoid these cracks.