It depends upon exactly where you step off.
The elevator, in order to remain in place, has to actually extend well past GEO. An object orbits based upon the speed at its center of mass. As you go down, orbital velocity required increases, and as you go up, it decreases... and the elevator also has an issue of as the elevator goes down from the center of mass, its speed decreases, and as you go up from the center of mass, speed increases. (Keeping in mind, down is towards the planet.)
Also, remember the laws of motion:
— An object in motion remains in motion until acted upon by an outside force.
Gravity is constantly acting, but the speed means that the pull isn't fast enough to bring one down, since gravity works over time.
So, if you step off 10m below the center of mass, you're in a decaying orbit already - the orbital speed needed is higher, but your retained orbital speed is lower. That difference is VERY small. Small enough to be ignored in the short term. But if you "hang" your tools nearby, and wander away, a few days later they've moved downward and trailing of the station, and will continue to do so, accelerating downward.
If you instead step off above the center of mass, you are above the orbital speed; you have attained escape velocity and will appear to arc away. It won't be a nice clean straight line, as you're close enough to orbital velocity that gravity keeps you curved. It will be a long slow spiral outward.
This effect, when maximized by a few kilometers, can be used, in theory, to launch interplanetary spacecraft.