The Ballymena men were drawn away to the Danske Bank Premiership side in this morning’s fifth round draw.
They will travel to Shamrock Park on January 9 after booking their place in the fifth round by beating Glebe Rangers on penalties at the weekend.
“It will obviously be a big ask against a hugely experienced team but we will enjoy the trip,” said Muir.
“But I’ve said all along that the priority for the club will be league surivial,” he added.
The Irish Cup game will also see a return to Shamrock Park for Wakehurst assistant manager Neil Candlish, who spent a number of seasons as a player with the County Armagh club.