The typical floor press is done with a barbell like in the video below. They also show a dumbbell variation.
One Arm Floor Press
With the single arm floor press the obvious option is a dumbbell. However, it isn’t the only option. Kettlebells are just as effective.
Getting into Position for a 1 Arm KB Floor Press
One Arm Bottom-Up Kettlebell Floor Press
Going bottoms-up means you’ll have to drop the weight. The stability isn’t there to press heavy weight. But, that’s also the magic of this lift and wh I like to add it to your workouts.
The instability created by the bottoms-up position forces the stabilize muscles of your shoulders to work harder compared to a barbell.