Use a telephoto lens, positioning you and camera several feet/meters away. Your reflection will be much smaller.
Can also use a mirror, which will effectively do same thing: position mirror on one side, then you and camera on other to reduce your reflection. Again, a telephoto lens and distance are your friends.
Based on the comments, I will explain the mirror application further: With mirrors, the distance you stand away from the mirror is the same as the distance which you must focus on the object in the mirror.
From the Physics Classroom:
For plane mirrors, the object distance (often represented by the symbol do) is equal to the image distance (often represented by the symbol di). That is the image is the same distance behind the mirror as the object is in front of the mirror. If you stand a distance of 2 meters from a plane mirror, you must focus at a location 2 meters behind the mirror in order to view your image.
This is often used in eye doctor offices for eye exams. An eye exam requires the patient to read a standard chart at a distance of 5 meters. But often, the facility does not have an examining room long enough to test distance vision, so instead, they have a mirror 2.5 meters in front of patient, and an eye chart on the wall behind the patient. Thus, they get the combined distance of 2x the room (patient to front mirror+front mirror to eye chart) for a total of 5m.
Therefore, by using a mirror, you can effectively reduce the overall size of your own reflection, without requiring significant physical distance between you and the spherical object.
The mirror can also help you to position where your reflection is located within the object. With mirrors, the angle of incidence equals the angle of reflection, allowing you to determine the position of your now smaller reflection where ever you like within the reflective sphere. Changing your approach angle to the mirror will change the position of your reflection within the sphere, perhaps off the side where it less noticeable.