Shaw has returned to Marine after making 17 appearances for the club, scoring one goal.
Wheeler has made 58 appearances across two spells with the club.
On the departures, joint-manager Kev Towey said: "Owen felt he needed a new challenge.
"By his own admission, his performances for most of the season have been well below the standard both he and the club have become accustomed to.
"He's a fantastic goalkeeper and I'm sure he'll have no issues finding a new club and rediscovering his form of previous seasons.
"Danny was approached by his former club Marine and being a Crosby lad, it was an offer he couldn't refuse on his door-step.
"The fact that this club is competing with the likes of Marine shows how far we've come in such a short space of time. It wasn't too long ago they were one of the best Non-League sides outside of the Conference."