First, as others say, it is an idiom. When someone hears or reads the phrase, their brain automatically parses it as the idiom they know, and does not notice the different endings.
Second, for me your variant while grammatically correct, would have a different meaning. The usual variant would mean "the subject is worthless" while your version would mean "the processing effort is too much". But as I already said, as this is an idiom, the most speakers would not notice that you modified the expression or would think this is a typo.
I also want to highlight that in certain interpretation your version can be seen as meaning something the opposite: the processing effort is so little that it even does not worth a sheep skin, if the sheep skin is meant to be not the subject of the work (on which the processing is done), but rather some small unit of value (and the subject of processing is omitted).
This may be understood so in circumstances where sheep skin is used as a currency, for instance. You can substitute here "копейка", so to get "копейки выделка не стоит" to mean the processing is very cheap.
In English you have a distinction between
The processing does not worth the sheep skin (skin is the subject of
The processing does not worth a sheep skin (skin is the unit of value)
Since Russian lacks articles, you can interpret this the both ways.
When you use the idiom the standard way, the ambiguity disappears.