Breast reduction amount and thoracic outlet syndrome. Would the procedure help with the numbness in my hands?

Thoracic Outlet syndrome results from excess pressure placed on a neurovascular bundle passing between the anterior and middle scalene muscles and can result in numbness like you described and sometimes affect the blood flow to your arms. It is not likely it will be improved with a breast reduction especially a small one (250 grams). See a thoracic surgeon who can determine if this is the right diagnosis. 

I'm not sure how breast reduction might help thoracic outlet syndrome. 250 g is a fairly small breast reduction.

Congratulations on your decision to proceed with breast reduction surgery; this operation tends to be one of the most patient pleasing operations we perform.  Unfortunately,  your situation is one where any relief of thoracic outlet syndrome symptoms cannot be accurately  predicted or guaranteed;  in other words, the symptoms of numbness in the hands, may or may not be alleviated by the breast reduction procedure.
I would suggest that you communicate your goals clearly with your plastic surgeon and make sure that you have realistic expectations prior to proceeding with any type of surgery. If necessary/helpful, seek consultation with additional plastic surgeons prior to making a decision about who to choose to perform the breast reduction procedure. Ask to see lots of examples of his/her work so you feel comfortable that he/she can achieve the outcome you are looking for. In regards to breast size desired, also communicate carefully. In my practice the use of goal pictures are helpful in this regard; a discussion of cup size can be confusing and imprecise.  For example, “C cup” or “proportionate" may mean different things to different people,  and therefore may be a source of miscommunication.    In other words, I would not suggest that you communicate your goals and/or base your satisfaction with the outcome of surgery on achieving a specific cup size.  Also, keep in mind that removal of a certain amount of tissue does not necessarily correspond to the achievement of a specific cup size. I hope this, and the attached link (dedicated to breast reduction concerns) helps. Best wishes.