i'm looking to lose bf%, not bulk up. is pushing weights/cardio before eating breakfast a good idea for this?

this morning i did approx 30mins of lifting, then tried out the new bikes at the gym for a 7min program. normally i'd do 25mins cardio though. then came home, ate breakfast. (8 eggwhite, 80g chick breast, 2 rice cakes, coffee) i'm looking to do this or a similar routine while on afternoon shifts.

so good idea or no? thanks