Is it necessary to send a corrigendum? Does it make my paper look ugly?
Given your clarifications 1, 2, and 3, I would suggest leaving it alone. 

The modern trend is for the corrigenda and the errata to be used more for "serious" stuff, and less so for "cosmetic" changes. The guideline, for example, given by the American Physiological Society is:


  if the author determines that it is scientifically necessary


While Nature uses the following definition for a corrigendum:


  Corrigendum. Notification of an important error made by the author(s) that affects the publication record or the scientific integrity of the paper, or the reputation of the authors or the journal. 


Unless the venue in which you published your work states otherwise in their publication guidelines, a stray sentence that is not factually false, does not invalidate your claims, and does not impinge on the efforts of other researchers to reproduce your work is likely not "scientifically necessary." 

Even if you insist on perfection, you should also be aware how corrigenda are viewed by other researchers in your field. If in your field the prevailing view is that corrigenda are used for "scientifically necessary" changes to your article, then you need to be prepared to answer questions about your correction in the future (usually of the form, "Why is there a corrigendum issued for your paper? Are you sure it doesn't change your conclusions?") 

Lastly, a minor point is that if you published in a journal which charges publication fees, quite often your corrigendum will come with a not-so-small price-tag also.