Katie Archibald leads the women's omnium at the halfway mark and her fellow Scot Mark Stewart is in points race action as Great Britain look to add to the two medals claimed so far on Friday's third day of action.
Skinner's sprint participation ended early. Six-time Olympic champion Jason Kenny was absent from Hong Kong on an extended post-Rio break, but Skinner has no regrets about competing after just three months' preparation.
"I'm just in a different place to where I was before Rio," said the 24-year-old Scot, runner-up to Jason Kenny last August.
"To come here and do a 9.9 (seconds in qualifying) and make it past the first round, I'll be honest, I am disappointed.
"I've tried to come into this competition without putting too much pressure on myself.
"It was a bonus to get selected and we've got some really nice long-term projects."
Nineteen riders qualified in under 10 seconds, with Skinner 15th-quickest in 9.969 seconds.
Skinner, who won Rio gold in the team sprint alongside Jason Kenny and Phil Hindes, appeared laboured in beating China's Xu Chao in the first round.
Second-fastest qualifier Max Niederlag was his next opponent.
The German was fresh after receiving a first-round bye and easily accelerated around Skinner to advance to Saturday's best-of-three quarter-finals.
Skinner added: "There's no more pressure than there was before. It's just the pressure shift.
"It used to be trying to fill Chris Hoy's shoes, trying to keep up with Jason and Phil (in the team sprint). And now it's about trying to continue the good results I had in Rio and make a name for myself."
Skinner may compete in one more event: the one-kilometre time-trial on Sunday's final day.
Ryan Owens did advance after qualifying in seventh place in 9.865. He beat Germany's Eric Engler and Hugo Barrette of Canada and will next face Niederlag.
Archibald was well-placed to add to Elinor Barker's scratch race silver on day one and Chris Latham's bronze in the corresponding men's event on Thursday.
With two-time Olympic omnium champion Laura Kenny (nee Trott) absent pregnant, expecting her first child with Jason Kenny, Archibald was given an individual focus here.
The Olympic team pursuit champion justified the call by winning both the scratch race and the tempo race to take an eight-point lead with two disciplines remaining in the omnium, which has been revised since Rio.
Matthew Bostock and Andy Tennant finished 13th and 14th, respectively, in the four-kilometres individual pursuit as Australia's Jordan Kerby clocked the third-fastest time in history in qualifying for the final.
Kerby finished in four minutes 12.172 seconds, behind only the world record of 4mins 10.534secs set by his compatriot Jack Bobridge in 2011 and Chris Boardman's previous best from 1996 of 4:11.114.
