I thought “Magic Sing” only made karaoke mics?
I would expect, for the purposes of recording, a proper recording microphone would outperform a karaoke microphone by a very large margin.
(there are many proper recording microphones available in the same price range as those karaoke mics).
If you can get a good “raw” (unprocessed) recording, not only does it save a lot of time in post production but the finished result is also likely to be much better. It is possible to compensate for poor recording and sometimes make considerable improvements, but it is very much better if you don’t need to.
A good recording environment is one of the key issues for making good recordings. Microphone placement is another.
There is a very long topic that discusses these issues here: budget (usb) mic for classical guitar recording needed