What's the deciding factor for which form of a word you choose before the word "skill"?
Solution 1:
My two cents:
I think when a gerund from a verb is possible, using 'gerund' seems to be more common.
negotiationnegotiating skills
(Internet)searchsearching skillsprogramprogramming skillswritewriting skills
When a gerund is not possible, a noun or an adjective seems to be common.
management skills
practical skills
technical skills
academic skills
As I said, this is not a concrete rule. I think taking help of authentic sources like Ngram would help you decide the correct form.