Is radioactive iodine a fairly safe treatment after total thyroidectomy for thyroid cancer? I'm 42 years old.

Radioactive iodine. It is safe and effective. It has been used millions of times and the side effects are low. It is being used more judiciously recently based on 2015 ATA guidelines. Low risk cancers don't usually need RAI. Intermediate risk can benefit from a low dose to ablate the thyroid remnant. High risk benefit from conventional RAI 70-100+ mCi.
Very safe . Radioactive iodine is a very safe and effective treatment even in young patients. It is one of the easiest and effective cancer treatments available.
Do it. This is routine after surgery for certain types and stages of thyroid cancer, is standard of care, has contributed to the fairly high cure rate even when these are quite aggressive, and if this was recommended to you by scientific physicians, you should do this without fear that there is anything they are not telling you.