Nope. Both fission AND fusion work because mass is converted to energy. In the case of fusion, the final fused atom weighs less than the two smaller atoms that were "fused"---that weight difference is the amount of mass converted to energy
In fission, the sum of the masses of the two atoms formed by the fission process is less than that of the original single fissionable atom. The weight difference again is the amount of mass converted to enery.
The same can be said about flashlight batteries. There will be a small change in mass between a new one and a depleted one due to energy conversion. It still doesn't change the fact that the main source of joy in a fission explosion is electromagnetic repulsion.