This is just me doing some freeform thinking around my personal experiences in Wado Ryu karate training as well as the minute amount of sword work I have done.

Extracting the sword from the "saya", the sheath, has to be made up of three parts, similar to the approach of karate technique application in Wado Ryu. You cannot imply pull the sword out with one arm, unless it's short that it. You can to pull the saya back and then turn the body to apply the cut or thrust.

Wado Ryu karate has its San Mi Ittai. Every application of technique brings together various aspects, unless you want to stand there and trade punches, which is also an option.