Answered by Shaykh Faraz Rabbani
Asslamoulaikoum,
I would like to know if we can read durood shareef without having wudhu? Or is it a big sign of disrespect upon nabi-e-kareem S.A.W to send durood upon him without wudhu?

Walaikum assalam wa rahmatullah,
I pray this finds you in the best of health and spirits.
It is superior adab and recommended to engage in remembrance of Allah–such as sending blessings upon the Messenger of Allah (peace and blessings be upon him)–while in a state of ritual purity.
However, this is not a condition for the permissibility of engaging in remembrance of Allah; and it is superior to busy oneself with remembrance of Allah while in a state of ritual impurity than not to. [Ibn Abidin, Radd al-Muhtar]
And Allah alone gives success.
Faraz Rabbani