As others have pointed out, in your examples, it is correct to use that, and not those.
Why? The that in your sentence is being used as a pronoun to introduce a relative restrictive clause, not as a pronoun referring to skills, so it doesn't get pluralized. Here's a helpful definition:
that (pronoun) \thət, ˈthat\ —18. used to introduce a restrictive relative clause ⇒ (e.g. the book that we want)
Essentially, your sentence
I have some skills that are useful in this situation.
is saying:
My skills are useful in this situation.
However, if you add the right punctuation, then the word that could be used as a pronoun referring to the subject of the sentence:
I have a skill (debating); that (skill) is useful in this situation.
And, in this case, the plural form would be used when referring to more than one skill:
I have skills (debating, logic, and public speaking); these (skills) are useful in this situation.
Furthermore, if you are talking about someone else's skills, you could change the these to those:
She has skills (debating, logic, and public speaking); those are useful in this situation.
Hopefully, I've provided some examples that are useful for your situation.
(or, I've provided some examples; hopefully, these are useful for your situation.)