Even if recommended by your doctor, it is always your choice not to have surgery. But, it is important to understand the possible consequences of delaying or declining surgery.
Because carpal tunnel release is an elective surgery, there are no serious or life-threatening consequences associated with not having it.
However, if other treatment methods have failed to improve your wrist condition and surgery has been recommended, it is likely that the current problems with your wrist will remain the same or even become worse. In other words, the likelihood of significant improvement without surgery is slim.
One consequence of delaying the surgery may be the continued damage to your median nerve. The longer the nerve is compressed and damaged, the less chance a full recovery can be obtained by surgical release. And without surgery, this can result in continued pain and persistent or worsening symptoms of numbness in the thumb, index and middle finger along with weakness and clumsiness of the hand.
The final decision to have or not to have surgery rests with you, but all concerns relating to this decision should be discussed with your doctor at length. Then you and your doctor can come up with a treatment method that is comfortable for you.