Well I'm sorry to hear the news about your tumor. Tumors in the brain cannot be outright removed without surgery, however the most common methods of treating tumors of the brain without surgical procedure is through radiation therapy or chemo. If your tumor is benign or cancerous, the methods may differ, and you must also factor in the position of the tumor in the brain (could it cause harm to vital structures?). Make sure to ask your oncologist or physician what methods they are considering and if you have options. Ideally, a little stay with radiation and some pills could shrink the growth. However if your doctor suggests that it must be removed, then hair shouldn't be on the top of your concern list. Your hair will probably be shaved, but it grows back. Brain cells that are destroyed by a tumor wont. Lets hope for the radiation and pills, though.