Celtic face a second 340-mile round trip to the Highlands in five days after the quarter-final was postponed on Sunday morning.
Neil Lennon’s men now face a Wednesday night clash against a team who drew at Parkhead in December.
That comes four days before their Co-operative Insurance Cup final against Rangers.
Ledley said: “It was disappointing, especially as we’d travelled up the day before. But I don’t think it will affect us because we came straight back in the morning and got to rest.”
Yesterday’s Scottish Cup semi-final draw paired Celtic — should they get past Inverness — with Aberdeen or St Mirren, while Dundee United or Motherwell will tackle the winners of Brechin City and St Johnstone.