Wa'alaykumsalaam
Yes we can read the Qur'an without Wudhu as agreed and proven.
The issue is, can we touch the Quran without wudhu?
Since this is a debatable question about the verse ' None should touch it except the pure one' where some scholars says it is about the touching of the Quran and some same it is about the book on the sacred tablet.
I would advice to have the wudhu while touching the Quran in order to be on the safe side and as well as the hadeeth “None is to touch the Qur’an except the pure.” may support us on that.
We do agree that sometimes we give Qur'an to none Muslims to read and all. They do not have wudhu but they still do read the Qur'an, so you may see the different opinion and areas here.
I would advice to perform wudhu before reading the Quran from mushaf and if ever your wudhu break, you may carry on reading it by not touching the arabic verses. This is my humble opinion.
Allah knows best