I'm aware that encryption of amateur radio communications is prohibited (or rather, any technique to make the message unreadable is). Does this apply to handheld transceivers ("Walkie-Talkies")?
Handheld transceivers are usually operated under some portion of 47 CFR 95 (Personal Radio Services). Typically, this is subpart B (Family Radio Service) or subpart D (CB Radio Service); occasionally it's subpart E (General Mobile Radio Service.
CB Radio Service only permits plain-language voice communication. Not only is encryption prohibited, using coded language is also forbidden (eg. the Navajo code talkers would be forbidden to communicate over CB radio).
Family Radio Service is slightly more permissive, permitting certain data transmissions in addition to voice, and it doesn't have the requirement of plain language. However, encryption is forbidden under the general prohibition of voice-obscuring features for Part 95 operation.
General Mobile Radio Service has a general prohibition on coded messages or messages with hidden meanings, making it possibly even more restrictive than CB radio's "plain language" requirement.