I can't speak to how much it would have cost, as that isn't my expertise. But, I can speak to the "how" mail was sent home. By the 1830s, well-established routes had been developed that Yankee whalers would frequent while on whaling voyages. A traditional first stop for whalers that had just rounded Cape Horn was Valparaiso, Chile. Often, whalers would stock up on fresh provisions there before venturing further out into the Pacific to hunt whales. If a crew member had written a letter to send home, he could leave it with another homeward-bound vessel, also provisioning in port, to be carried home and delivered ashore. Likewise, it was not uncommon to come across another whaling vessel while at sea. In this instance, often the two vessels would heave-to a short distance away from each other and row out in whaleboats to meet eachother and exchange news if one of the vessels had recently come from home (called a "Gam"). This was the primary means of obtaining news while at sea as well as delivering letters. There was no formalized method of delivering mail internationally from a whaling vessel, so letters were passed from ship to ship and eventually would end up at its destination, though often many months after its writing. It was a haphazard system at best, but one in which the sailors had come to rely.

Sources: Francis Allyn Olmstead, Incidents of a Whaling Voyage (New York, D. Appleton and Co.), 1841.

Nathaniel Philbrick, In the Heart of the Sea (New York, Penguin Books), 2000.