Even though it is said they need Wight for Cersei, the true reason is that they need it for everyone really. As time goes by more and more people are starting to accept it as a real threat, but only those who survived the Others understand the true danger. Daenerys kind of wants to listen to Jon after a while, but abandoning the war because of the legend of White Walkers is not the move she will make without this proof either. If she (or anyone else) really believed him and comprehend what kind of danger is actually coming, she would head for the Wall without wasting a minute.
So when they arrive at Eastwatch, Tormund asks Jon which queen he needs to convince, Jon replies: "Both". I think that is the heart of the matter. Furthermore, as Sam said, Citadel can make a large movement of armies, resources, and information if they would believe Others are coming. Other big or lesser lords and people, in general, may come around with news of such proof.
For Jon: he knows he won't succeed in defending the Wall with small numbers he has. He needs Daenerys first since she has more than 100k soldiers and has dragons, but he needs all Westeros really.
For Daenerys and Tyrion: they need to suspend a war with Cersei first as Daenerys won't go north since the war for the throne is more important to her. Tyrion knows Cersei also wants to get some time after the last defeat, so there is a chance. But as Jon said, even Tyrion doesn't really believe in Night King, so bringing Wight to the south will surely be very beneficial.
And no, it is not less risky to simply go with dragons to the Wall. There are many similar questions around like she just flies over with dragon and burns the Others. Truth is, Night King is too smart for that, plus he obviously has some magic powers. And we don't know what kind of aces he may keep hidden, millions of soldiers, giants, he can bring a horrible storm that will put down even dragons, etc. So, as lieutenant Stansfield in "Leon, the Professional" said: "Bring me everyone. EVERYONE!!!!!"