The Lambs, a representative side made up from pupils at independent schools, will play four matches in the South American country.
They will open their tour with a match against Uruguay on March 27 before taking on a Buenos Aires Select XV on March 29. Their big match will come on March 31 when they play Argentina Under-18s. They will end their tour with a fixture against San Isidro Club on April 2.
The Lambs have taken 25 players to Argentina – 15 forwards and 10 backs.
Rayworth (pictured) is a centre, who has already played three times for the Lambs.
Hampden-Smith is a second-row, who has four caps for the Lambs.
Lambs’ national director Alex Laybourne said: “We have selected a very exciting squad to take to Argentina; one which will be able to play ‘fast and free’ as well as matching the South American physicality that we are expecting.
“The players will be challenged in four tough fixtures, but will also have the tour of a lifetime both on and off the field.”