If a person is, Heaven forbid, confined to a wheelchair, may he be pushed through a public domain on Shabbat in a place without an Erub?
It is clear that the patient is allowed to push himself, and that it is forbidden for him to have a Jew push him. But is it permissible to have a non-Jew push a wheelchair through a public domain on Shabbat?
Hacham Ovadia Yosef addresses this question in his Yabia Omer (9:34), where he writes (listen to audio recording for precise citation) that one may ask a non-Jew to push him on a wheelchair on Shabbat to attend prayers in the synagogue. He notes that according to some authorities, most public domains today do not qualify as a Halachic "Reshut Ha’rabim" with respect to the laws of Shabbat, since there are not 600,000 people going through the area. As such, according to this view, carrying in a public domain today is forbidden only on the level of Rabbinic enactment (Mi’de’rabbanan). And there is a rule regarding the laws of Shabbat that one may ask a gentile to perform an action which is forbidden for Jews Mi’de’rabbanan, if this is necessary for the sake of a Misva ("Shebut De’shbut Be’makom Misva"). Hacham Ovadia adds that even according to the view that carrying in our public domains is forbidden on the level of Torah law, the Ba’al Ha’ittur was of the opinion that for the sake of the Misva one may ask a gentile to perform even acts forbidden by the Torah. Although we do not generally follow this view, we have here a "Sefek Sefeka" ("double doubt"), as there are two Halachic controversies at play, each of which with an opinion that would allow having a gentile push one in a wheelchair for the sake of a Misva, such as to pray with a Minyan.
It should be noted that cosmopolitan areas such as Brooklyn may, indeed, qualify as a "Reshut Ha’rabim" according to all opinions, given the high volume of traffic that passes through. As such, Hacham Ovadia’s rationale clearly does not apply. Nevertheless, in places where an Erub has been erected, even for those who do not accept the Erub’s validity and do not allow carrying within it, the Erub likely has the effect of lowering the level of carrying to that of a Rabbinic prohibition. As such, in these areas one would be able to have a gentile push a wheelchair through the public domain on Shabbat for the sake of a Misva.
Summary: In areas where carrying on Shabbat is forbidden only Mi’de’rabbanan (by force of Rabbinic enactment), one may ask a gentile to push a person on a wheelchair for the sake of a Misva, such as to pray with a Minyan. This applies in suburban areas and small towns. In cosmopolitan areas, if an Erub was erected, even those who do not rely on it for carrying may allow a gentile to push somebody in a wheelchair for the sake of a Misva.