Former World Championship semi-finalist swail was the highest profile player in the first round, and the 42-year-old will aim to continue his progress at the expense of Day on Saturday morning.
John Parkin's 4-1 win over Ricky Norris earned him a tough test in the second round in the form of Stephen Lee, while Rod Lawler awaits Itaro Santos after the Brazilian saw off Stephane Ochoiski by the same margin.
2010 Crucible champion Neil Robertson will begin his tournament against Alex Taubman, who progressed after defeating Elliot Slessor 4-2, and Ashley Carty's 4-0 sweep of Dean Goddard sets up a meeting with Joe Perry.
The first session of round two contests begins on Friday morning and features Stephen Maguire, Mark King and Mark Davis in action.
Round one results
Phil O'Kane 4-2 Andrew Milliard
Tom Maxfield 2-4 Adam Wicheard
Ashley Carty 4-0 Dean Goddard
Lucky Vatnani 1-4 Oliver Lines
Matthew Day 4-3 Steven Hallworth
William Lemons 1-4 John Astley
Alex Taubman 4-2 Elliot Slessor
Ricky Norris 1-4 John Parkin
Itaro Santos 4-1 Stephane Ochoiski
Mitchell Mann 4-2 Nico Elton
Hans Blanckaert 2-4 James Cahill
Wan Chooi Tan 0-4 Christopher Norbury
Sam Harvey 4-0 Jack Bradford
Jamie Gibson 0-4 Kyren Wilson
Joe Swail 4-0 Ross Higgins