Cassidy made the announcements to the media on Thursday morning.
Lindholm was hit hard by Hurricanes forward Andrei Svechnikov during the second period of Game 2 of the first-round series on Wednesday night and did not return.
Swayman, meanwhile, gets the nod over Linus Ullmark, who has allowed nine goals through two starts in the series. The 23-year-old posted a 23-14-3 record with a 2.41 goals-against average and a .914 save percentage across 41 appearances in the regular season.
The Hurricanes lead the best-of-seven series, 2-0.