Yes going outside in the first week is a very bad idea. However not because the radiation outside will instantly drop you. Much of the radiation will be coming from radioactive dust, known as fallout that’ll be comprised of all kinds of isotopes. The isotopes that decay quickly release a lot of radiation over a short period and if you go outside you will come back covered in them. This will bring radiation into wherever you are using as your shelter. This would not just harm the person who went outside but everyone else sheltering with them. So do not go outside for any reason. You can make do without power for a while.
On a related note; keep water and food covered. Skin is a surprisingly good defense against radiation but breathing in this dust or letting it get into the food you eat or the water you drink is very dangerous. After a week has passed you should for your own safety keep the time spent outside your shelter as low as possible. Short trips outside will become safer as time goes on but activities that kick up dust will still be dangerous for a long time.