Q. Is a father of a newborn baby allowed to wear the hospital ID on the bracelet in a place where there is no eiruv? Is it similiar to the case of a prisoner wearing chains in 301:19 or similiar to the case of green circle in 301:23 which one is permitted to wear outside? Or perhaps similar to what Rav Moshe writes in Orach chaim 1:111 about watches that anything that is worn on the guf is called a malbish and one is permitted to go out with? During the time the baby is in the hospital, the father  wears it the entire time even during sleep. Or  perhaps is it similar to a  moch dochuk which  assur to wear outside? Thanks in advance.

A. Although, Igrois Moshe (O. H. 1: 111), ruled that in principle one is permitted to carry a watch on Shabbos because it is considered an article of clothing, and is similar to a ring with a signet, however, many Poskim disagree and the minhag today is to be stringent. (Chelkas Yaakov 2: 97 et. al. See also Igros Moshe Y.D. 2: 47 on moch dochuk). Shemiras Shabbos Kehilchoso (40: 32) maintains that one should not wear an ID bracelet where there is no eruv.
However, Chashukei Chemed (Shabbos 52b) in regards to hospital ID bands rules that in need, one may rely on the Igrois Moshe, especially when we dealing with a karmelis.
Horav Shlomo Miller’s Shlit’a opinion is similar to be lenient in need, when the ID band will remain on the hand of the father, until the discharge of the baby. The Rov does distinguish between a watch, where the item carried has an ongoing operative working purpose of functioning and showing the changing time, it could stop working and thus become a maso, as opposed to the ID bracelet, that just serves by being there, and thus maintains its malbush status.
(See also question 1412, in regards to wearing a red string on the street on Shabbos)

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a