Such a long trip just after the Australian Open for an away tie played on clay at altitude looked a potentially unappealing prospect, but Cameron Norrie, Dan Evans, Draper, Joe Salisbury and Neal Skupski have all made themselves available.
Norrie and Evans will be favoured for the singles rubbers, but 42nd-ranked Draper, who recently turned 21, could make his debut in the competition at the Pueblo Viejo Country Club just outside Bogota.
Skupski is part of the world number one doubles pair with Dutchman Wesley Koolhof, while Salisbury sits just behind him in the rankings and is a five-time grand slam champion.
Arguably the most disappointing week of Smith's long tenure as captain came in September when Britain lost to the USA and the Netherlands in Glasgow and failed to qualify for the quarter-finals.
Following the tie, Evans went public with his disgruntlement about not being picked for the doubles rubbers, which did not go down well with his team-mates, and Smith will need to ensure there is no hangover.
The winners of the tie, which will be played on February 3-4, will qualify for the group stage in September, where Britain are again in line to be a host country provided they are involved.