What is the best word or phrase for expressing that 2 skills are unrelated to each other?
When factors are independent, they can be called orthogonal, fancy for a 90-degree relationship (right angled). They don't feed each other, they don't interact, they don't conflict.
Statistically independent: mental ability may be classified into several orthogonal … factors — O. D. Duncan - Merriam-Webster dictionary online
Use this word abstractly when you want to say "I'm not fighting you. Our opinions differ, that's all. They're orthogonal."
Nontransferable
Software development skills are nontransferable to engineering management skills.
It beats variations on the unrelated word you already rejected by speaking directly to the idea that the knowledge or skills of one are not transferred to or shared by the other. This word/idea of transfer is common in sports skill training and is applicable here.
You may also use the term "independent".
Independent [in-di-pen-duh nt] /adjective
- not dependent; not depending or contingent upon something else for existence, operation, etc.
Source: Dictionary.com
This term may be best used when you are talking about how the separate skill sets are each exclusive from the other. You can acquire one, the other, or both. There is no collaborative value that increases either skill set themselves, nor is the cumulative value greater than the sum of each skill sets own value.
Some things are related, but can still be independent. Therefore, the term independent is useful in that it is less focused on the relational similarity of the subject matter and more to do with how they interact.
"Software development skills and engineering management skills are independent of each other..."
I think the word you want is "disparate".
Essentially different in kind; not able to be compared.
‘they inhabit disparate worlds of thought’
I think this works well in your sentence:
Software development skills are [completely] disparate to engineering management skills. Learning one doesn't help you learn the other.