Is one permitted to wear a wristwatch on Shabbat in an area that does not have an Eruv?

In the halachic rulings of the Sh’mirat Shabbat K’Hilchata (Chapter 18: S’if 26,and S’if Katan 45) HaRav Shlomo Zalman Auerbach is cited as contending that since the wristwatch is worn on a regular basis it is considered as if it is part of one’s clothing. Accordingly, it is permissible to be worn on Shabbat even in areas that lack an Eruv. Rav Auerbach was requested to finely hone his ruling. Namely, was it permitted L’chatchila according to halacha to wear a wristwatch in an area without an Eruv or did the Rav state his position merely as a means (Bid’ieved) to suggest that one should not protest against those who wore such watches on Shabbat. Rav Auerbach responded that he believed that it was permissible according to the halacha(Al pi din, L’chatchila). Yet, should one wish to be stringent there is support for such a position also. (V’A’laihu Lo Yeebol, Customs of HaRav Shlomo Zalman Auerbach,Volume I:Siman 220). Rabbi J. Simcha Cohen