Battered by Hurricane Sandy, this seaside getaway is being rebuilt with a radically redesigned telephone system — a glimpse of future technology that many residents say they don’t want. Verizon, the only phone company in town, wants most of the island and its 500 homes to go all-wireless, ending for good its century-old copper wire phone network. That means phone lines buried underground or strung between poles and then stretched into homes will go out of service and be replaced by an experimental wireless service that sends calls between cell towers and home receivers. Although it carries only voice calls today, the new technology is a harbinger for faster, more capable mobile and Internet services expanding across the nation. Phone giants Verizon and AT&T have let some of their traditional phone networks atrophy and have put tens of billions of dollars into the mobile and high-speed land-line Internet services that generate more revenue.