The British team, without Andy Murray for the first time since his recent retirement, has a different feel for the Davis Cup Finals group stage event.
Dan Evans and Neal Skupski, who memorably teamed up to secure a “bonkers” doubles victory which put Britain through to the eight-team knockout stage in Manchester last year, remain in the squad alongside Draper and provide experience.
But Billy Harris – a late bloomer who has just moved to a career-high 101st in the world aged 29 – and 28-year-old Wimbledon doubles champion Henry Patten could be handed debuts.
British number two Cameron Norrie is missing through the arm injury which ruled him out of the recent US Open.
Smith praised Draper’s commitment to playing for his nation despite the short turnaround from his exploits in New York.
Draper had strapping applied to his right thigh before hitting with British number 10 Charles Broom for about an hour in Manchester.
“He is really excited to come here but we have to get him on the practice court, see how he’s doing, assess him,” added Smith, speaking on Tuesday before Draper linked up with the squad.
“Ultimately I’ll make the call on that. I have to select the team to do what is best, not just for tomorrow, but also we have really important matches at the weekend as well.
“We just have to weigh up risk versus reward a little bit.
“We have four guys here who are more than capable of going out tomorrow if that’s required and doing a really good job.”
Smith’s squad face Finland, Argentina and Canada in the round-robin event at Manchester’s AO Arena.
The top two teams progress to the eight-nation finals which will be held in Malaga between 19-24 November.