Cameron Norrie will lead Great Britain in their Davis Cup play-off against Colombia after the nation's top five ranked players were selected.
That means there is no place for former world number one Andy Murray in captain Leon Smith's team in Bogota next month.
Britain failed to qualify for the quarter-finals last year following defeats by the USA and the Netherlands.
British number one Norrie is ranked 14th in the world, while Evans (27) and Draper (42) are also ranked inside the top 50.
Skupski is the world number one doubles player - alongside Dutch team-mate Wesley Koolhof - a couple of places ahead of five-time grand slam champion Salisbury.