Yep. You're limited to the original skillset.
The big difference between this and the Can't Live Without is that in this, you're trying to minimize all skills at once. In the can't live without, you could play through once and use no climbers but 99 of everything else, then again using no floaters but 99 of everything else, and in the end come up with something like only one builder that was common to *all* the solutions.
This one, on the other hand, you're trying to come up with one solution that, as much as possible, avoids using the same skills repeatedly.
In that one, if the current record was 2 Climbers, 3 Builders, and you could solve the level with only 2 builders by using a 3rd climber, you'd have improved the result because you still used less builders. In this one, you'd still be using one skill three times (even if you're changing which skill it is), so a 3 climber 2 builder solution would be no better (but, of course, no worse) than a 2 climber 3 builder one.
If you look at the can't live without, for example, Fun 20 is listed as 1 builder. However, in this topic, the minimum is two - you may be able to beat it with only one (or even none) of any *specific* skill; but for an entire skillset for the level, there will have to be at least one skill that you have at least two of - in the case of Fun 20, I actually used two of *every* skill to acheive that result, except floaters.
Hopefully I'm making it clear what I mean? This is somewhat a hard concept for me to put into words...