Play was suspended late Thursday due to dangerous weather with several groups unable to complete the first round. Fisher still has two holes to play in his first round.
Dyson holds the clubhouse lead after a bogey-free 7-under-par 65 while Fisher was also without a bogey heading into No. 17.
Jared Harvey, Ross Fisher and Erik Van Rooyen completed their rounds at 6-under 66 while Darren Fichardt and Danie Van Tonder were both 6-under through 17 holes.
Six more players, including Kevin Phelan who had played only 14 holes, are tied for eighth at 5-under.
Dyson was 3-under through 14 holes and jumped ahead with a closing string of four birdies. After a birdie at the par-5 15th, he pitched to within 1 foot at 16, dropped a 15-foot putt at 17 and ended with a 25-foot birdie putt.
Fisher's round included four birdies in a five-hole span over Nos. 7-11. He still has 17 and 18 to play in the first round. The 18th hole, a 497-yard par 4, is playing as the third-toughest so far in the tournament.
The tournament is being played on the 7,964-yard Copperleaf Golf and Country Estate course, which is the longest on the European Tour.