Both the English alphabet version and the katakana version are okay.
You can choose whichever you like.
There is no definite rule for that. I don't think there is such deep meaning in choosing which, as you are worrying about.
As for "scrub," I only knew it is a verb meaning "washing very hardly" or a noun to refer to the clothes that ER doctors wear. Anyway, at the top of the lyrics, the definition is shown, so we can understand what it means.
In my case, I'm okay to see the katakana or the alphabets or the Japanese translations such as つまらない男.
If you google "TLC No Scrubs 和訳" in Google Japan, you will get a lot of translations.
(I cannot show the web pages here because these sites include the video, which is restricted by the forum rule.)
For example, I'll quote the first four websites' translations for "I don't want no (any) scrub."
( I just realized that "I don't want no scrub" had an error of the double negative, whose meaning was actually the opposite.)
1. scrubなんて必要ないわ
2."スクラブ"なんていらないわ
3. つまらない男はいらないわ
4. スクラブなんてお断り
As you can see, all English alphabets, katakana, or Japanese translations are adopted by translators.
1, 2, and 3 adopt "わ" because, in the Japanese colloquial expression, women use feminine wording, accompanied by わ at the end of a sentence.
スクラブなんて必要ないわ sounds much more natural than スクラブなんて必要ない because this should be colloquial.
In a formal setting, スクラブなど必要ない would be better because なんて is a colloquial expression.
必要ない(わ)、いらない(わ) and お断り(お断りわ is wrong though) have the same meaning.
Hope this helps!