Sesshoumaru is somewhat able to weild Tetsusaiga. As indirectly stated in episode 7 (Showdown-Inuyasha vs Sesshoumaru), Inuyasha is able to weild the tetsusaiga because he cared for humans. In the episode 134 (The Women who Loved Sesshoumaru-part 2) Sesshoumaru was somewhat able to weild Tetsusaiga to save the soul (to my understanding) of the women whom loved him. His hand was a little burned (it didn't seem to hurt him though). While in the 3rd movie, Sesshoumaru weilded Tetsusaiga to attack Inuyasha (I think it was because he was angry that caused Tetsusaiga's barrier hurted him more than it did when in episode 134). Well, that's what I think.
Submitted by Just a person who was looking around the site