I'm not a doctor (if you want your question answered by a doctor, you have to post it to the "ask a doctor" tab at the top of your screen).
I am, however, a 5+ year thyroid cancer survivor and have done a lot of personal research into the topic. In my opinion, I think your sister should absolutely listen to the doctors' advice and get the surgery. I've seen studies that say that the two best predictors of good outcome with thyroid cancer is aggressiveness of treatment and young age. Your sister is 25 (a year older than I was when I had my treatment). She's in good shape there.
In my opinion and from all I've read from every respected medical source, yes, the surgery is the only solution. This isn't something that can be shrunk with radiation or anything like that. Besides, that would probably be worse on her. Delaying surgery would only give the cancer a chance to grow more a possibly spread. There is absolutely no reason to wait. Nothing good will come of waiting. There are no new treatments on the horizon or anything like that. Thyroid cancer is very very treatable if it is found early and treated aggressively.
Every operation has risks, but this one is minimally risky, as long as she has a good surgeon. I'm sure the doctors have gone over the risks with her. At this point, waiting is more risky than the operation.
After the surgery, she's going to be without a thyroid (they are going to do a total thyroidectomy, right?) and so she will have to be on hormone replacement for the rest of her life, but many people (including myself) live with that without issue. Just a pill every morning and she'll be fine, ready to live life normally.
Do not, I repeat, do not discourage her from going through with the surgery because of your fears. The doctors know what is best and I'm sure she is being told about all the risks and the after-effects. Ask her questions and be there for her, but this is something that needs to be done to give her the best chance to never have to go through this again. If you have more questions or if she does, please feel free to post.
I wish your sister and you all the best.