The Medicare application is not hard to fill out, typically only taking about 10 minutes, according to the Social Security Administration. It's possible to sign up for Medicare online and submit the application electronically with no need to visit a Social Security office.
When the Medicare enrollment form is accessed online, no forms have to be signed. An enrollee can start the application, pause it and return to finish at a later time. Typically, an enrollee fills out the form, submits it electronically and then receives his Medicare card in the mail. The SSA only contacts an enrollee if more information is required. It's possible to sign up for Medicare without simultaneously receiving Social Security benefits, as the Social Security Administration points out.