There's an exponential identity that you can use instead of expanding it all out.
e^{\hat{-\hat{B}}}\hat{A}e^{\hat{B}} = \hat{A} + [A,B] + 1/2![A,[A,B]] + 1/3![A,[A,[A,B]]] + ...
Because often times, the dagger of a unitary operator is just the negative of it. And the...