There are two choices given by the dictionaries (both Oxford and Merriam-Webster).
https://www.youtube.com/watch?v=h4WuwXZaGgo
(Merriam-Webster)
https://www.youtube.com/watch?v=OnVXWrZV4yE
(Oxford)
How Do You Pronounce Uranus?
https://www.youtube.com/watch?v=SQTKGXmITZg
“How do astronomers and scientists say the name of the 7th planet from the Sun?”
That’s the traditional, non-libertine way (Ur-in-us), which is also closer to the Greek but easier for Americans to say. Of the people from the sciences in the third video, the Lebanese in the medical school was the exception. Note his behavior. What a surprise. Enough said.
It’s so cute that in the third video you linked, no matter how serious and scholarly these people are, they still noticeably blush when this question is asked, just from thinking about what the one guy called “the giggle factor.”