The Rama (Rabbi Moshe Isserless, Poland, 1525-1572) writes (301:23; listen to audio for precise citation) that one may not walk in a public domain with a cloth used for cleaning his nose, unless it is sewn onto to his garment. If the handkerchief is sewn to the garment, it loses its independent status and becomes part of the garment. The person is thus seen as wearing, rather than carrying, the handkerchief, and he may therefore walk with it in a public domain on Shabbat.
However, Chacham Bentzion Abba Shaul (Jerusalem, 1924-1998) held that this ruling does not apply to modern-day handkerchiefs, which are of a higher quality and thus do not become secondary to one's garment. Even if a person sews his handkerchief to his garment, the handkerchief retains its stature as an independent entity, as something external to the garment itself. Therefore, today it is forbidden to walk in a public domain with a handkerchief, even if the handkerchief is sewn to one's garments. Certainly, one may not walk in a public domain on Shabbat with a handkerchief in his pocket, whether he carries it in his pants pocket or in his jacket breast pocket for decoration.
Summary: One may not walk in a public domain with a handkerchief, even if it is sewn to his garment, except where there is a proper Eruv.
