DTLS-SRTP builds on DTLS which applies its own encryption layer. The handshake, by construction, is done outside of any encryption, and that's fine.
"Relay servers" are a red herring. The two clients will talk to each other by sending data packets which will go through a number of other systems. Whether you consider some of these systems as "routers" or as "relays" does not matter; security properties ensured by TLS (and DTLS) don't depend on the actual transport method.
Inserting PGP keys in the mixture does any good only if you want to use these keys as basis for authentication. This is theoretically possible, meaning that the protocol has been defined -- but it remains to be actually implemented and deployed. With this support, the X.509-based certificates of SSL are replaced with PGP public keys; this maps to DTLS as well. Getting rid of X.509 certificates is a good idea if you have other means to achieve mutual authentication, and PGP keys can be such means, as RFC 6091 describes.